doHB: Estimate a Hierarchical Bayesian Model
In RSGHB: Functions for Hierarchical Bayesian Estimation: A Flexible Approach
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
The user can initiate the model estimation by calling the doHB function. The function will optionally perform initial diagnostic tests to look for common errors in specifying the model. Upon completion, the function will optionally write a number of output files with the model parameters and convergence statistics to the user's working directory.
The flexibility comes in allowing the user to specify the likelihood function directly instead of assuming predetermined model structures. Types of models that can be estimated with this code include the family of discrete choice models (Multinomial Logit, Mixed Logit, Nested Logit, Error Components Logit and Latent Class) as well as ordered response models like ordered probit and ordered logit. In addition, the package allows for flexibility in specifying parameters as either fixed (non-varying across individuals) or random with continuous distributions. Parameter distributions supported include normal, positive/negative log-normal, positive/negative censored normal and the Johnson SB distribution.
Kenneth Train's Matlab and Gauss code for doing Hierarchical Bayesian estimation has served as the basis for a few of the functions included in this package. (See references below).
Usage
1
doHB(likelihood_user, choicedata, control = list())
Arguments
likelihood_user
A function that returns likelihood values for each observation in your data set. This function must accept arguments fc and b, representing the fixed parameters and individual parameters, respectively, and computes the likelihood of observing the data given those values.
choicedata
A data.frame of choice data to be used in estimation. Minimally requires an 'ID' column associated with the vector of likelihoods returned by likelihood_user.
control
A list of estimation controls. See below for more details.
Details
The fc argument to the likelihood_user function is a numeric vector of length length(gVarNamesFixed). It is NULL if gVarNamesFixed is NULL.
The b argument to the likelihood_user function is a numeric matrix with length(gVarNamesNormal) columns and length(likelihood_user(...)) rows. In other words, one column per random parameter and one row per choice task. It is NULL if gVarNamesNormal is NULL.
There are a number of global variables that can be set to control the model estimation. Some need to be specified directly in the model control list while others have default values that can be adjusted by the analyst if something other than the default is desired.
User-specified controls
constraintsNorm - A list of monotonic constraints to be applied during estimation. The structure of the constraints is c(param1number, inequality, param2number). For constraints relative to 0, use 0 instead of param2number. For inequality, use 1 for < and 2 for >.
For example constraintsNorm = list(c(5,1,0), c(6,1,5), c(7,1,6)) would constrain the 5th parameter < 0, the 6th parameter < 5th parameter, and the 7th parameter < the 6th parameter. If NULL, no constraints are used. (Defaults to NULL)
degreesOfFreedom - Additional degrees of freedom for the prior variance-covariance matrix, not including the number of parameters. (Defaults to 5)
FC - A vector of starting values for the fixed parameters. There should be an element for each name in gVarNamesFixed. (Defaults to rep(0, length(gVarNamesFixed)))
fixedA - Fixes the means of the underlying normal distribution of random variables to certain values as opposed to estimating them. This would be important for example in an error components logit model or an integrated choice and latent variable model. The format for this input is a vector of length equal to the number of random parameters. Use NA for variables that should be estimated, e.g., fixedA = c(NA, NA, NA, NA, NA, NA, NA, 0). In this case, the mean of the underlying normal for the 8th random variable would be fixed to 0. If NULL, all means are estimated. (Defaults to NULL)
fixedD - Fixes the variance of the underlying normal distribution of the random variables to certain values as opposed to estimating them. This would be important for example in an integrated choice and latent variable model. The format for this input is a vector of length equal to the number of random parameters. Use NA for variables that should be estimated, e.g., fixedD = c(NA, NA, NA, NA, NA, NA, NA, 1). In this case, the variance of the underlying normal for the 8th random variable would be fixed to 1. If NULL, all variances are estimated. (Defaults to NULL)
gDIST - A vector of integers (1-6) that indicate which type of distribution should be applied to the random parameters. 1 = Normal, 2 = Postive Log-Normal, 3 = Negative Log-Normal, 4 = Positive Censored Normal, 5 = Negative Censored Normal, 6 = Johnson SB. There should be an element for each name in gVarNamesNormal. (Defaults to rep(1, length(gVarNamesNormal)))
gFULLCV - Indicates whether a full variance-covariance structure should be used for the random parameters. (Defaults to TRUE)
gINFOSKIP - Number of iterations between printing/plotting information about the iteration process. (Defaults to 250)
gMAXCOEF - A vector of maximums for the Johnson SB distributions. If Johnson SB is used, each random coefficent needs an element but only the elements that correspond to a JSB in gDIST are used. (Defaults to 0)
gMINCOEF - A vector of minimums for the Johnson SB distributions. If Johnson SB is used, each random coefficent needs an element but only the elements that correspond to a JSB in gDIST are used. (Defaults to 0)
gNCREP - Number of burn-in iterations to use prior to convergence. (Defaults to 100000)
gNEREP - Number of iterations to keep for averaging after convergence has been reached. (Defaults to 100000)
gNSKIP - Number of iterations in between retaining draws for averaging. (Defaults to 1)
gVarNamesFixed - A character vector of names for the fixed parameters. (REQUIRED)
gVarNamesNormal - A character vector of names for the random parameters. (REQUIRED)
gStoreDraws - Whether to store the draws for the individual level parameters. Doing so can dramatically increase the memory usage of the model if there are a large number of individuals or draws. (Defaults to FALSE)
hIW - A boolean indicating if a hierarchical Inverted Wishart should be used when sampling in posterior distribution for the covariance matrix. New in version 1.2.0. (Defaults to FALSE)
modelname - The model name which is used for creating output files. (Defaults to "HBModel")
nodiagnostics - If TRUE, an initial diagnostic report and prompt is not reported to the screen. This makes batch processing more seamless. (Defaults to FALSE)
priorVariance - The prior variance assumed. Ignored if pvMatrix is not NULL. (Defaults to 2)
pvMatrix - A custom prior variance-covariance matrix to be used in estimation. The prior variance-covariance matrix needs to be a matrix object and of the correct size: length(gVarNamesNormal) by length(gVarNamesNormal). If provided, overrides priorVariance. (Defaults to NULL)
rho - The initial proportionality fraction for the jumping distribution of the Metropolis-Hastings algorithm for the random parameters. This fraction is adjusted after each iteration to target an acceptance rate of targetAcceptanceNormal. (Defaults to 0.1)
rhoF - The proportionality fraction for the jumping distribution for the Metropolis-Hastings algorithm for the fixed parameters. This fraction is adjusted after each iteration to target an acceptance rate of targetAcceptanceFixed. (Defaults to 0.0001)
svN - A vector of starting values for the means of the underlying normals for the random parameters. There should be an element for each name in gVarNamesNormal. (Defaults to rep(0, length(gVarNamesNormal)))
targetAcceptanceFixed - The target acceptance rate in the Metropolis-Hastings algorithm for the fixed parameters. (Defaults to 0.3)
targetAcceptanceNormal - The target acceptance rate in the Metropolis-Hastings algorithm for the random parameters. (Defaults to 0.3)
verbose - Whether estimation information should be printed/plotted during the iteration process. (Defaults to TRUE)
writeModel - Indicates whether the model results should be written as a series of CSV files to the working directory upon estimation completion. (Defaults to FALSE, see writeModel)
Value
a model object of class RSGHB. Contains:
modelname
A character string identifying the model.
params.fixed
A character vector naming the estimated fixed parameters.
params.vary
A character vector naming the estimated random parameters.
distributions
A character vector of assumed distributions for each random parameter.
pv
The prior variance-covariance matrix assumed for estimation.
df
Additional degrees of freedom in the model.
gNP
The number of individuals in the model.
gOBS
The number of observations in the model.
gNCREP
The number of burn-in iterations used prior to convergence.
gNEREP
The number of iterations used for averaging.
constraints
A list of constraints. (see 'Details' above)
iter.detail
A data.frame of model statistics at every gINFOSKIP'th iteration.
A
A matrix containing the sample-level means of the underlying normals at each iteration. Is NULL if no random parameters were estimated.
B, Bsd
A matrix containing the mean individual-level draws across iterations for the underlying normals. The Bsd object provides the standard deviations of these individual draws. Is NULL if no random parameters were estimated.
C, Csd
A matrix containing the mean individual-level draws across iterations for the underlying normals while including the appropriate distribution transformations. The Csd object provides the standard deviations of these individual draws. Is NULL if no random parameters were estimated.
D
An array of the sample variance-covariance matrix for each iteration. Is NULL if no random parameters were estimated.
F
A matrix containing the set of fixed (non-random) parameters at each iteration. Is NULL if no fixed parameters were estimated.
choices
A vector of choices if provided.
p
A vector of probabilities at the mean values of C and F.
ll0
The initial log-likelihood given the starting values of sVN and FC.
llf
The final log-likelihood at the mean values of C and F.
Author(s)
Jeffrey Dumont <jeff.dumont@rsginc.com>, Jeff Keller <jeff.keller@rsginc.com>
References
Train, K. (2009) Discrete Choice Methods with Simulation. Cambridge University Press.
Train, K. and Sonnier G. (2005) Mixed Logit with Bounded Distributions of Correlated Partworths, Applications of Simulation Methods in Environmental and Resource Economics. Edited by Anna Alberini and Riccardo Scarpa. http://elsa.berkeley.edu/~train/trainsonnier.pdf
Train, K. Original Gauss and Matlab code: http://elsa.berkeley.edu/Software/abstracts/train1006mxlhb.html
See Also
Examples
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# Organize choicedata for modeling
data(choicedata)
tt1 <- choicedata$tt1
tt2 <- choicedata$tt2
toll2 <- choicedata$toll2
choice1 <- (choicedata$Choice==1)
choice2 <- (choicedata$Choice==2)
# The model likelihood function
likelihood <- function(fc, b) {
# Assign Beta vectors to named parameters for convenience
cc <- 1
wtp1 <- b[, cc]; cc <- cc + 1
price <- b[, cc]; cc <- cc + 1
# Discrete choice utility in WTP-space
v1 <- price * wtp1 * tt1
v2 <- price * toll2 + price * wtp1 * tt2
# Return the probability of choice
p <- (exp(v1)*choice1 + exp(v2)*choice2) / (exp(v1) + exp(v2))
return(p)
}
# Estimation controls/settings
control <- list(
modelname = "MNL_WTPSpace",
gVarNamesNormal = c("WTP", "Price"),
gNCREP = 300,
gNEREP = 100,
gINFOSKIP = 10,
gNSKIP = 2,
nodiagnostics = TRUE
)
# Estimate the model
set.seed(1987)
model <- doHB(likelihood, choicedata, control)
Example output
Loading required package: MCMCpack
Loading required package: coda
Loading required package: MASS
##
## Markov Chain Monte Carlo Package (MCMCpack)
## Copyright (C) 2003-2019 Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park
##
## Support provided by the U.S. National Science Foundation
## (Grants SES-0350646 and SES-0350613)
##
Diagnostic checks passed. Please review before proceeding
-----------------------------------------------------------
Number of Individuals: 1138
Number of Observations: 10242
Prior variance: 2
Target Acceptance (Normal): 0.3
Degrees of Freedom: 5
Avg. Number of Observations per Individual: 9
Initial Log-Likelihood: -7099.213423
-----------------------------------------------------------
Random Parameters Start Dist.
WTP 0 N
Price 0 N
-----------------------------------------------------------
Choice Matrix
Count %
1 6682 0.65
2 3560 0.35
-----------------------------------------------------------
Iteration: 1
-----------------------------------------------------------
RHO (Normal): 0.11
Acceptance Rate (Normal): 0.5
Parameter RMS: 0.2443457094
Avg. Variance: 0.04734285079
Log-Likelihood: -6957.584041
RLH: 0.5086367502
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.009371821
Price: -0.025427158
-----------------------------------------------------------
Time per iteration: Calculating...
Time to completion: Calculating...
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 10
-----------------------------------------------------------
RHO (Normal): 0.259374246
Acceptance Rate (Normal): 0.6862917399
Parameter RMS: 0.262517561
Avg. Variance: 0.04615571446
Log-Likelihood: -6590.010923
RLH: 0.5289412398
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05101558
Price: -0.05761182
-----------------------------------------------------------
Time per iteration: 0.0244 secs
Time to completion: 0.199 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 20
-----------------------------------------------------------
RHO (Normal): 0.6727499949
Acceptance Rate (Normal): 0.5755711775
Parameter RMS: 0.2758766024
Avg. Variance: 0.04602836272
Log-Likelihood: -6492.524467
RLH: 0.5352811079
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04534017
Price: -0.11236858
-----------------------------------------------------------
Time per iteration: 0.00518 secs
Time to completion: 0.0414 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 30
-----------------------------------------------------------
RHO (Normal): 1.744940227
Acceptance Rate (Normal): 0.3857644991
Parameter RMS: 0.2753653717
Avg. Variance: 0.04471576586
Log-Likelihood: -6417.76856
RLH: 0.5394821602
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04952143
Price: -0.13688866
-----------------------------------------------------------
Time per iteration: 0.00511 secs
Time to completion: 0.04 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 40
-----------------------------------------------------------
RHO (Normal): 2.478887852
Acceptance Rate (Normal): 0.3207381371
Parameter RMS: 0.2720625985
Avg. Variance: 0.05147839875
Log-Likelihood: -6397.076152
RLH: 0.5402388242
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.0462136
Price: -0.1733574
-----------------------------------------------------------
Time per iteration: 0.0139 secs
Time to completion: 0.106 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 50
-----------------------------------------------------------
RHO (Normal): 2.357397682
Acceptance Rate (Normal): 0.2855887522
Parameter RMS: 0.2722019479
Avg. Variance: 0.05063214595
Log-Likelihood: -6339.856731
RLH: 0.5439869765
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01953859
Price: -0.21579848
-----------------------------------------------------------
Time per iteration: 0.00483 secs
Time to completion: 0.0362 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 60
-----------------------------------------------------------
RHO (Normal): 2.241861739
Acceptance Rate (Normal): 0.3567662566
Parameter RMS: 0.2764390867
Avg. Variance: 0.06313342568
Log-Likelihood: -6347.651173
RLH: 0.5430444561
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01141959
Price: -0.23790466
-----------------------------------------------------------
Time per iteration: 0.0048 secs
Time to completion: 0.0352 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 70
-----------------------------------------------------------
RHO (Normal): 2.605763364
Acceptance Rate (Normal): 0.3312829525
Parameter RMS: 0.2710969876
Avg. Variance: 0.06143699572
Log-Likelihood: -6362.973162
RLH: 0.5422146586
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.009828258
Price: -0.250698586
-----------------------------------------------------------
Time per iteration: 0.00483 secs
Time to completion: 0.0346 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 80
-----------------------------------------------------------
RHO (Normal): 2.027499572
Acceptance Rate (Normal): 0.2996485062
Parameter RMS: 0.2764993471
Avg. Variance: 0.06769038661
Log-Likelihood: -6325.983248
RLH: 0.5443907577
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.008622545
Price: -0.282523399
-----------------------------------------------------------
Time per iteration: 0.00503 secs
Time to completion: 0.0352 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 90
-----------------------------------------------------------
RHO (Normal): 2.356605679
Acceptance Rate (Normal): 0.3260105448
Parameter RMS: 0.2839082366
Avg. Variance: 0.07329111296
Log-Likelihood: -6285.719778
RLH: 0.5462002534
-----------------------------------------------------------
Random Parameters Estimate
WTP: -0.009063934
Price: -0.319521571
-----------------------------------------------------------
Time per iteration: 0.00477 secs
Time to completion: 0.0326 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 100
-----------------------------------------------------------
RHO (Normal): 2.739132674
Acceptance Rate (Normal): 0.3066783831
Parameter RMS: 0.2938470669
Avg. Variance: 0.08237665634
Log-Likelihood: -6305.936849
RLH: 0.5453471285
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01012956
Price: -0.32946904
-----------------------------------------------------------
Time per iteration: 0.00481 secs
Time to completion: 0.0321 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 110
-----------------------------------------------------------
RHO (Normal): 2.604887919
Acceptance Rate (Normal): 0.295254833
Parameter RMS: 0.2946394543
Avg. Variance: 0.08322545039
Log-Likelihood: -6291.331493
RLH: 0.5461513284
-----------------------------------------------------------
Random Parameters Estimate
WTP: -0.001526503
Price: -0.325496441
-----------------------------------------------------------
Time per iteration: 0.0049 secs
Time to completion: 0.0318 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 120
-----------------------------------------------------------
RHO (Normal): 2.477222492
Acceptance Rate (Normal): 0.2917398946
Parameter RMS: 0.3001366273
Avg. Variance: 0.09002404864
Log-Likelihood: -6312.697449
RLH: 0.5447851977
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.0023286
Price: -0.3501747
-----------------------------------------------------------
Time per iteration: 0.00479 secs
Time to completion: 0.0303 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 130
-----------------------------------------------------------
RHO (Normal): 2.87932815
Acceptance Rate (Normal): 0.3198594025
Parameter RMS: 0.317051085
Avg. Variance: 0.1053465311
Log-Likelihood: -6284.707853
RLH: 0.5463612097
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01375754
Price: -0.38822913
-----------------------------------------------------------
Time per iteration: 0.00505 secs
Time to completion: 0.0311 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 140
-----------------------------------------------------------
RHO (Normal): 3.34670407
Acceptance Rate (Normal): 0.3014059754
Parameter RMS: 0.3195821539
Avg. Variance: 0.1115147892
Log-Likelihood: -6279.501021
RLH: 0.5461415314
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01438638
Price: -0.39086709
-----------------------------------------------------------
Time per iteration: 0.00487 secs
Time to completion: 0.0292 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 150
-----------------------------------------------------------
RHO (Normal): 2.604012767
Acceptance Rate (Normal): 0.2724077329
Parameter RMS: 0.3308794156
Avg. Variance: 0.1208708807
Log-Likelihood: -6284.016778
RLH: 0.5459580514
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03457599
Price: -0.40813379
-----------------------------------------------------------
Time per iteration: 0.00486 secs
Time to completion: 0.0283 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 160
-----------------------------------------------------------
RHO (Normal): 3.026699172
Acceptance Rate (Normal): 0.3031634446
Parameter RMS: 0.323654504
Avg. Variance: 0.1130006151
Log-Likelihood: -6251.300867
RLH: 0.5478097461
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.02113844
Price: -0.39927396
-----------------------------------------------------------
Time per iteration: 0.00485 secs
Time to completion: 0.0275 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 170
-----------------------------------------------------------
RHO (Normal): 2.35502247
Acceptance Rate (Normal): 0.2961335677
Parameter RMS: 0.3293062923
Avg. Variance: 0.1196142668
Log-Likelihood: -6255.468032
RLH: 0.547786205
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.02745202
Price: -0.40345593
-----------------------------------------------------------
Time per iteration: 0.00485 secs
Time to completion: 0.0267 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 180
-----------------------------------------------------------
RHO (Normal): 2.737292477
Acceptance Rate (Normal): 0.3189806678
Parameter RMS: 0.3356223851
Avg. Variance: 0.1240324656
Log-Likelihood: -6250.325365
RLH: 0.5480194497
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.02135741
Price: -0.41179847
-----------------------------------------------------------
Time per iteration: 0.00493 secs
Time to completion: 0.0263 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 190
-----------------------------------------------------------
RHO (Normal): 2.60313791
Acceptance Rate (Normal): 0.3391915641
Parameter RMS: 0.3343096851
Avg. Variance: 0.1211071643
Log-Likelihood: -6278.892705
RLH: 0.5466303187
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.0158434
Price: -0.4136840
-----------------------------------------------------------
Time per iteration: 0.0138 secs
Time to completion: 0.0713 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 200
-----------------------------------------------------------
RHO (Normal): 2.475558251
Acceptance Rate (Normal): 0.2987697715
Parameter RMS: 0.3433928396
Avg. Variance: 0.1269764728
Log-Likelihood: -6270.992243
RLH: 0.5470646818
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01557675
Price: -0.40061774
-----------------------------------------------------------
Time per iteration: 0.00479 secs
Time to completion: 0.0239 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 210
-----------------------------------------------------------
RHO (Normal): 2.877393767
Acceptance Rate (Normal): 0.3040421793
Parameter RMS: 0.3465950065
Avg. Variance: 0.1307444441
Log-Likelihood: -6267.266255
RLH: 0.547053059
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01573064
Price: -0.40481985
-----------------------------------------------------------
Time per iteration: 0.00483 secs
Time to completion: 0.0233 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 220
-----------------------------------------------------------
RHO (Normal): 2.736372842
Acceptance Rate (Normal): 0.3057996485
Parameter RMS: 0.3587176313
Avg. Variance: 0.1436690142
Log-Likelihood: -6202.197798
RLH: 0.5508132206
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03151904
Price: -0.42015661
-----------------------------------------------------------
Time per iteration: 0.00495 secs
Time to completion: 0.0231 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 230
-----------------------------------------------------------
RHO (Normal): 2.602263346
Acceptance Rate (Normal): 0.2794376098
Parameter RMS: 0.3874735134
Avg. Variance: 0.1680813896
Log-Likelihood: -6209.863932
RLH: 0.5505157645
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.02550019
Price: -0.47043068
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.022 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 240
-----------------------------------------------------------
RHO (Normal): 2.474726549
Acceptance Rate (Normal): 0.3189806678
Parameter RMS: 0.3776896113
Avg. Variance: 0.1596189741
Log-Likelihood: -6222.284227
RLH: 0.5498800404
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03578634
Price: -0.45992533
-----------------------------------------------------------
Time per iteration: 0.00489 secs
Time to completion: 0.0212 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 250
-----------------------------------------------------------
RHO (Normal): 2.353440325
Acceptance Rate (Normal): 0.2741652021
Parameter RMS: 0.3636392058
Avg. Variance: 0.1493022531
Log-Likelihood: -6242.442354
RLH: 0.5487430808
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03329289
Price: -0.43999711
-----------------------------------------------------------
Time per iteration: 0.00477 secs
Time to completion: 0.0199 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 260
-----------------------------------------------------------
RHO (Normal): 2.735453516
Acceptance Rate (Normal): 0.2688927944
Parameter RMS: 0.3705459799
Avg. Variance: 0.1559512501
Log-Likelihood: -6235.561288
RLH: 0.5486691149
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03339947
Price: -0.45816968
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.0195 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 270
-----------------------------------------------------------
RHO (Normal): 2.601389076
Acceptance Rate (Normal): 0.2855887522
Parameter RMS: 0.3849031848
Avg. Variance: 0.1630008291
Log-Likelihood: -6228.984457
RLH: 0.5496331684
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.02760512
Price: -0.47367304
-----------------------------------------------------------
Time per iteration: 0.00484 secs
Time to completion: 0.0185 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 280
-----------------------------------------------------------
RHO (Normal): 3.0236496
Acceptance Rate (Normal): 0.3057996485
Parameter RMS: 0.3947922074
Avg. Variance: 0.1744267078
Log-Likelihood: -6249.033566
RLH: 0.5483138937
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03317348
Price: -0.47609350
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.0179 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 290
-----------------------------------------------------------
RHO (Normal): 2.352649651
Acceptance Rate (Normal): 0.2943760984
Parameter RMS: 0.3967730381
Avg. Variance: 0.1755300487
Log-Likelihood: -6238.288487
RLH: 0.5491907592
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03517681
Price: -0.47475612
-----------------------------------------------------------
Time per iteration: 0.00498 secs
Time to completion: 0.0174 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 300
-----------------------------------------------------------
RHO (Normal): 2.734534499
Acceptance Rate (Normal): 0.309314587
Parameter RMS: 0.396286579
Avg. Variance: 0.178924374
Log-Likelihood: -6241.989956
RLH: 0.5486498317
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04380939
Price: -0.45858404
-----------------------------------------------------------
Time per iteration: 0.00481 secs
Time to completion: 0.016 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 310
-----------------------------------------------------------
RHO (Normal): 2.6005151
Acceptance Rate (Normal): 0.2776801406
Parameter RMS: 0.4005202601
Avg. Variance: 0.1826253697
Log-Likelihood: -6221.174193
RLH: 0.5500535593
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04619759
Price: -0.50043058
-----------------------------------------------------------
Time per iteration: 0.00494 secs
Time to completion: 0.0157 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 320
-----------------------------------------------------------
RHO (Normal): 2.473063985
Acceptance Rate (Normal): 0.295254833
Parameter RMS: 0.4026059938
Avg. Variance: 0.1840046035
Log-Likelihood: -6207.475939
RLH: 0.550838876
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04578772
Price: -0.49049084
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.0147 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 330
-----------------------------------------------------------
RHO (Normal): 2.874494629
Acceptance Rate (Normal): 0.3145869947
Parameter RMS: 0.3903394667
Avg. Variance: 0.1701092072
Log-Likelihood: -6211.49385
RLH: 0.5508800074
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04043269
Price: -0.47824114
-----------------------------------------------------------
Time per iteration: 0.00489 secs
Time to completion: 0.0139 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 340
-----------------------------------------------------------
RHO (Normal): 2.236594738
Acceptance Rate (Normal): 0.2943760984
Parameter RMS: 0.3916609956
Avg. Variance: 0.1721631282
Log-Likelihood: -6203.357388
RLH: 0.5509781514
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04685106
Price: -0.48457618
-----------------------------------------------------------
Time per iteration: 0.00492 secs
Time to completion: 0.0131 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 350
-----------------------------------------------------------
RHO (Normal): 2.599641418
Acceptance Rate (Normal): 0.2891036907
Parameter RMS: 0.3876331996
Avg. Variance: 0.1670445092
Log-Likelihood: -6178.188181
RLH: 0.5521206664
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03520622
Price: -0.46867893
-----------------------------------------------------------
Time per iteration: 0.0135 secs
Time to completion: 0.0338 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 360
-----------------------------------------------------------
RHO (Normal): 2.472233121
Acceptance Rate (Normal): 0.2891036907
Parameter RMS: 0.3974743256
Avg. Variance: 0.1812562915
Log-Likelihood: -6237.433884
RLH: 0.5488422421
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04847559
Price: -0.48805959
-----------------------------------------------------------
Time per iteration: 0.00481 secs
Time to completion: 0.0112 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 370
-----------------------------------------------------------
RHO (Normal): 2.3510691
Acceptance Rate (Normal): 0.2891036907
Parameter RMS: 0.4016339987
Avg. Variance: 0.1854971898
Log-Likelihood: -6239.960169
RLH: 0.549140605
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04257693
Price: -0.49265862
-----------------------------------------------------------
Time per iteration: 0.00477 secs
Time to completion: 0.0103 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 380
-----------------------------------------------------------
RHO (Normal): 2.732697391
Acceptance Rate (Normal): 0.30228471
Parameter RMS: 0.4100367937
Avg. Variance: 0.1962747582
Log-Likelihood: -6230.07327
RLH: 0.5491135704
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05405504
Price: -0.50787303
-----------------------------------------------------------
Time per iteration: 0.00498 secs
Time to completion: 0.00996 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 390
-----------------------------------------------------------
RHO (Normal): 2.598768029
Acceptance Rate (Normal): 0.2873462214
Parameter RMS: 0.417165855
Avg. Variance: 0.2020739328
Log-Likelihood: -6182.791457
RLH: 0.5519658415
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04811652
Price: -0.51914157
-----------------------------------------------------------
Time per iteration: 0.0052 secs
Time to completion: 0.00953 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 400
-----------------------------------------------------------
RHO (Normal): 2.471402537
Acceptance Rate (Normal): 0.2811950791
Parameter RMS: 0.4165320641
Avg. Variance: 0.203120914
Log-Likelihood: -6200.198157
RLH: 0.5507549761
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04161142
Price: -0.53561482
-----------------------------------------------------------
Time per iteration: 0.00493 secs
Time to completion: 0.00822 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 410
-----------------------------------------------------------
RHO (Normal): 2.872563494
Acceptance Rate (Normal): 0.3075571178
Parameter RMS: 0.407394919
Avg. Variance: 0.1936872594
Log-Likelihood: -6237.696447
RLH: 0.548901719
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05279738
Price: -0.52214365
-----------------------------------------------------------
Time per iteration: 0.00482 secs
Time to completion: 0.00723 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 420
-----------------------------------------------------------
RHO (Normal): 2.235092155
Acceptance Rate (Normal): 0.2987697715
Parameter RMS: 0.4166975822
Avg. Variance: 0.2026367784
Log-Likelihood: -6211.456375
RLH: 0.5504695076
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04844027
Price: -0.53422111
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.00651 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 430
-----------------------------------------------------------
RHO (Normal): 2.597894933
Acceptance Rate (Normal): 0.3101933216
Parameter RMS: 0.4130540822
Avg. Variance: 0.1968258702
Log-Likelihood: -6211.278103
RLH: 0.5506168281
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04932911
Price: -0.52620975
-----------------------------------------------------------
Time per iteration: 0.00486 secs
Time to completion: 0.00567 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 440
-----------------------------------------------------------
RHO (Normal): 3.019588284
Acceptance Rate (Normal): 0.3084358524
Parameter RMS: 0.4193359481
Avg. Variance: 0.2049347772
Log-Likelihood: -6215.13207
RLH: 0.5506200561
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05515558
Price: -0.51345618
-----------------------------------------------------------
Time per iteration: 0.00484 secs
Time to completion: 0.00484 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 450
-----------------------------------------------------------
RHO (Normal): 2.871598413
Acceptance Rate (Normal): 0.3040421793
Parameter RMS: 0.4236825038
Avg. Variance: 0.207800636
Log-Likelihood: -6219.87991
RLH: 0.5499500632
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.0526718
Price: -0.5310368
-----------------------------------------------------------
Time per iteration: 0.0049 secs
Time to completion: 0.00408 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 460
-----------------------------------------------------------
RHO (Normal): 2.730861518
Acceptance Rate (Normal): 0.3057996485
Parameter RMS: 0.4148841118
Avg. Variance: 0.2024618865
Log-Likelihood: -6205.166952
RLH: 0.5508063027
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05368845
Price: -0.51361749
-----------------------------------------------------------
Time per iteration: 0.00485 secs
Time to completion: 0.00323 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 470
-----------------------------------------------------------
RHO (Normal): 2.597022131
Acceptance Rate (Normal): 0.3268892794
Parameter RMS: 0.4182879148
Avg. Variance: 0.2016471529
Log-Likelihood: -6198.583489
RLH: 0.5512758293
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05611717
Price: -0.53006742
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.00244 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 480
-----------------------------------------------------------
RHO (Normal): 2.469742206
Acceptance Rate (Normal): 0.309314587
Parameter RMS: 0.4196575616
Avg. Variance: 0.2069126384
Log-Likelihood: -6185.995692
RLH: 0.5519201977
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05772128
Price: -0.52757466
-----------------------------------------------------------
Time per iteration: 0.0049 secs
Time to completion: 0.00163 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 490
-----------------------------------------------------------
RHO (Normal): 2.348700264
Acceptance Rate (Normal): 0.2811950791
Parameter RMS: 0.4219524381
Avg. Variance: 0.2122793557
Log-Likelihood: -6191.760395
RLH: 0.5514095925
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.06871362
Price: -0.53411055
-----------------------------------------------------------
Time per iteration: 0.0136 secs
Time to completion: 0.00226 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 500
-----------------------------------------------------------
RHO (Normal): 2.729944043
Acceptance Rate (Normal): 0.3145869947
Parameter RMS: 0.4156325427
Avg. Variance: 0.2011661706
Log-Likelihood: -6213.70571
RLH: 0.5503714364
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05525883
Price: -0.52521068
-----------------------------------------------------------
Time per iteration: 0.00482 secs
Time to completion: 0 mins
-----------------------------------------------------------
Estimation complete.
RSGHB documentation built on July 4, 2019, 1:02 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
The user can initiate the model estimation by calling the doHB function. The function will optionally perform initial diagnostic tests to look for common errors in specifying the model. Upon completion, the function will optionally write a number of output files with the model parameters and convergence statistics to the user's working directory.
The flexibility comes in allowing the user to specify the likelihood function directly instead of assuming predetermined model structures. Types of models that can be estimated with this code include the family of discrete choice models (Multinomial Logit, Mixed Logit, Nested Logit, Error Components Logit and Latent Class) as well as ordered response models like ordered probit and ordered logit. In addition, the package allows for flexibility in specifying parameters as either fixed (non-varying across individuals) or random with continuous distributions. Parameter distributions supported include normal, positive/negative log-normal, positive/negative censored normal and the Johnson SB distribution.
Kenneth Train's Matlab and Gauss code for doing Hierarchical Bayesian estimation has served as the basis for a few of the functions included in this package. (See references below).
Usage
1 | doHB(likelihood_user, choicedata, control = list())
|
Arguments
likelihood_user |
A function that returns likelihood values for each observation in your data set. This function must accept arguments |
choicedata |
A data.frame of choice data to be used in estimation. Minimally requires an 'ID' column associated with the vector of likelihoods returned by |
control |
A list of estimation controls. See below for more details. |
Details
The fc argument to the likelihood_user function is a numeric vector of length length(gVarNamesFixed). It is NULL if gVarNamesFixed is NULL.
The b argument to the likelihood_user function is a numeric matrix with length(gVarNamesNormal) columns and length(likelihood_user(...)) rows. In other words, one column per random parameter and one row per choice task. It is NULL if gVarNamesNormal is NULL.
There are a number of global variables that can be set to control the model estimation. Some need to be specified directly in the model control list while others have default values that can be adjusted by the analyst if something other than the default is desired.
User-specified controls
constraintsNorm - A list of monotonic constraints to be applied during estimation. The structure of the constraints is c(param1number, inequality, param2number). For constraints relative to 0, use 0 instead of param2number. For inequality, use 1 for < and 2 for >.
For example constraintsNorm = list(c(5,1,0), c(6,1,5), c(7,1,6)) would constrain the 5th parameter < 0, the 6th parameter < 5th parameter, and the 7th parameter < the 6th parameter. If NULL, no constraints are used. (Defaults to NULL)
degreesOfFreedom - Additional degrees of freedom for the prior variance-covariance matrix, not including the number of parameters. (Defaults to 5)
FC - A vector of starting values for the fixed parameters. There should be an element for each name in gVarNamesFixed. (Defaults to rep(0, length(gVarNamesFixed)))
fixedA - Fixes the means of the underlying normal distribution of random variables to certain values as opposed to estimating them. This would be important for example in an error components logit model or an integrated choice and latent variable model. The format for this input is a vector of length equal to the number of random parameters. Use NA for variables that should be estimated, e.g., fixedA = c(NA, NA, NA, NA, NA, NA, NA, 0). In this case, the mean of the underlying normal for the 8th random variable would be fixed to 0. If NULL, all means are estimated. (Defaults to NULL)
fixedD - Fixes the variance of the underlying normal distribution of the random variables to certain values as opposed to estimating them. This would be important for example in an integrated choice and latent variable model. The format for this input is a vector of length equal to the number of random parameters. Use NA for variables that should be estimated, e.g., fixedD = c(NA, NA, NA, NA, NA, NA, NA, 1). In this case, the variance of the underlying normal for the 8th random variable would be fixed to 1. If NULL, all variances are estimated. (Defaults to NULL)
gDIST - A vector of integers (1-6) that indicate which type of distribution should be applied to the random parameters. 1 = Normal, 2 = Postive Log-Normal, 3 = Negative Log-Normal, 4 = Positive Censored Normal, 5 = Negative Censored Normal, 6 = Johnson SB. There should be an element for each name in gVarNamesNormal. (Defaults to rep(1, length(gVarNamesNormal)))
gFULLCV - Indicates whether a full variance-covariance structure should be used for the random parameters. (Defaults to TRUE)
gINFOSKIP - Number of iterations between printing/plotting information about the iteration process. (Defaults to 250)
gMAXCOEF - A vector of maximums for the Johnson SB distributions. If Johnson SB is used, each random coefficent needs an element but only the elements that correspond to a JSB in gDIST are used. (Defaults to 0)
gMINCOEF - A vector of minimums for the Johnson SB distributions. If Johnson SB is used, each random coefficent needs an element but only the elements that correspond to a JSB in gDIST are used. (Defaults to 0)
gNCREP - Number of burn-in iterations to use prior to convergence. (Defaults to 100000)
gNEREP - Number of iterations to keep for averaging after convergence has been reached. (Defaults to 100000)
gNSKIP - Number of iterations in between retaining draws for averaging. (Defaults to 1)
gVarNamesFixed - A character vector of names for the fixed parameters. (REQUIRED)
gVarNamesNormal - A character vector of names for the random parameters. (REQUIRED)
gStoreDraws - Whether to store the draws for the individual level parameters. Doing so can dramatically increase the memory usage of the model if there are a large number of individuals or draws. (Defaults to FALSE)
hIW - A boolean indicating if a hierarchical Inverted Wishart should be used when sampling in posterior distribution for the covariance matrix. New in version 1.2.0. (Defaults to FALSE)
modelname - The model name which is used for creating output files. (Defaults to "HBModel")
nodiagnostics - If TRUE, an initial diagnostic report and prompt is not reported to the screen. This makes batch processing more seamless. (Defaults to FALSE)
priorVariance - The prior variance assumed. Ignored if pvMatrix is not NULL. (Defaults to 2)
pvMatrix - A custom prior variance-covariance matrix to be used in estimation. The prior variance-covariance matrix needs to be a matrix object and of the correct size: length(gVarNamesNormal) by length(gVarNamesNormal). If provided, overrides priorVariance. (Defaults to NULL)
rho - The initial proportionality fraction for the jumping distribution of the Metropolis-Hastings algorithm for the random parameters. This fraction is adjusted after each iteration to target an acceptance rate of targetAcceptanceNormal. (Defaults to 0.1)
rhoF - The proportionality fraction for the jumping distribution for the Metropolis-Hastings algorithm for the fixed parameters. This fraction is adjusted after each iteration to target an acceptance rate of targetAcceptanceFixed. (Defaults to 0.0001)
svN - A vector of starting values for the means of the underlying normals for the random parameters. There should be an element for each name in gVarNamesNormal. (Defaults to rep(0, length(gVarNamesNormal)))
targetAcceptanceFixed - The target acceptance rate in the Metropolis-Hastings algorithm for the fixed parameters. (Defaults to 0.3)
targetAcceptanceNormal - The target acceptance rate in the Metropolis-Hastings algorithm for the random parameters. (Defaults to 0.3)
verbose - Whether estimation information should be printed/plotted during the iteration process. (Defaults to TRUE)
writeModel - Indicates whether the model results should be written as a series of CSV files to the working directory upon estimation completion. (Defaults to FALSE, see writeModel)
Value
a model object of class RSGHB. Contains:
modelname |
A character string identifying the model. |
params.fixed |
A character vector naming the estimated fixed parameters. |
params.vary |
A character vector naming the estimated random parameters. |
distributions |
A character vector of assumed distributions for each random parameter. |
pv |
The prior variance-covariance matrix assumed for estimation. |
df |
Additional degrees of freedom in the model. |
gNP |
The number of individuals in the model. |
gOBS |
The number of observations in the model. |
gNCREP |
The number of burn-in iterations used prior to convergence. |
gNEREP |
The number of iterations used for averaging. |
constraints |
A list of constraints. (see 'Details' above) |
iter.detail |
A data.frame of model statistics at every |
A |
A matrix containing the sample-level means of the underlying normals at each iteration. Is |
B, Bsd |
A matrix containing the mean individual-level draws across iterations for the underlying normals. The |
C, Csd |
A matrix containing the mean individual-level draws across iterations for the underlying normals while including the appropriate distribution transformations. The |
D |
An array of the sample variance-covariance matrix for each iteration. Is |
F |
A matrix containing the set of fixed (non-random) parameters at each iteration. Is |
choices |
A vector of choices if provided. |
p |
A vector of probabilities at the mean values of |
ll0 |
The initial log-likelihood given the starting values of |
llf |
The final log-likelihood at the mean values of |
Author(s)
Jeffrey Dumont <jeff.dumont@rsginc.com>, Jeff Keller <jeff.keller@rsginc.com>
References
Train, K. (2009) Discrete Choice Methods with Simulation. Cambridge University Press.
Train, K. and Sonnier G. (2005) Mixed Logit with Bounded Distributions of Correlated Partworths, Applications of Simulation Methods in Environmental and Resource Economics. Edited by Anna Alberini and Riccardo Scarpa. http://elsa.berkeley.edu/~train/trainsonnier.pdf
Train, K. Original Gauss and Matlab code: http://elsa.berkeley.edu/Software/abstracts/train1006mxlhb.html
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | # Organize choicedata for modeling
data(choicedata)
tt1 <- choicedata$tt1
tt2 <- choicedata$tt2
toll2 <- choicedata$toll2
choice1 <- (choicedata$Choice==1)
choice2 <- (choicedata$Choice==2)
# The model likelihood function
likelihood <- function(fc, b) {
# Assign Beta vectors to named parameters for convenience
cc <- 1
wtp1 <- b[, cc]; cc <- cc + 1
price <- b[, cc]; cc <- cc + 1
# Discrete choice utility in WTP-space
v1 <- price * wtp1 * tt1
v2 <- price * toll2 + price * wtp1 * tt2
# Return the probability of choice
p <- (exp(v1)*choice1 + exp(v2)*choice2) / (exp(v1) + exp(v2))
return(p)
}
# Estimation controls/settings
control <- list(
modelname = "MNL_WTPSpace",
gVarNamesNormal = c("WTP", "Price"),
gNCREP = 300,
gNEREP = 100,
gINFOSKIP = 10,
gNSKIP = 2,
nodiagnostics = TRUE
)
# Estimate the model
set.seed(1987)
model <- doHB(likelihood, choicedata, control)
|
Example output
Loading required package: MCMCpack
Loading required package: coda
Loading required package: MASS
##
## Markov Chain Monte Carlo Package (MCMCpack)
## Copyright (C) 2003-2019 Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park
##
## Support provided by the U.S. National Science Foundation
## (Grants SES-0350646 and SES-0350613)
##
Diagnostic checks passed. Please review before proceeding
-----------------------------------------------------------
Number of Individuals: 1138
Number of Observations: 10242
Prior variance: 2
Target Acceptance (Normal): 0.3
Degrees of Freedom: 5
Avg. Number of Observations per Individual: 9
Initial Log-Likelihood: -7099.213423
-----------------------------------------------------------
Random Parameters Start Dist.
WTP 0 N
Price 0 N
-----------------------------------------------------------
Choice Matrix
Count %
1 6682 0.65
2 3560 0.35
-----------------------------------------------------------
Iteration: 1
-----------------------------------------------------------
RHO (Normal): 0.11
Acceptance Rate (Normal): 0.5
Parameter RMS: 0.2443457094
Avg. Variance: 0.04734285079
Log-Likelihood: -6957.584041
RLH: 0.5086367502
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.009371821
Price: -0.025427158
-----------------------------------------------------------
Time per iteration: Calculating...
Time to completion: Calculating...
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 10
-----------------------------------------------------------
RHO (Normal): 0.259374246
Acceptance Rate (Normal): 0.6862917399
Parameter RMS: 0.262517561
Avg. Variance: 0.04615571446
Log-Likelihood: -6590.010923
RLH: 0.5289412398
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05101558
Price: -0.05761182
-----------------------------------------------------------
Time per iteration: 0.0244 secs
Time to completion: 0.199 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 20
-----------------------------------------------------------
RHO (Normal): 0.6727499949
Acceptance Rate (Normal): 0.5755711775
Parameter RMS: 0.2758766024
Avg. Variance: 0.04602836272
Log-Likelihood: -6492.524467
RLH: 0.5352811079
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04534017
Price: -0.11236858
-----------------------------------------------------------
Time per iteration: 0.00518 secs
Time to completion: 0.0414 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 30
-----------------------------------------------------------
RHO (Normal): 1.744940227
Acceptance Rate (Normal): 0.3857644991
Parameter RMS: 0.2753653717
Avg. Variance: 0.04471576586
Log-Likelihood: -6417.76856
RLH: 0.5394821602
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04952143
Price: -0.13688866
-----------------------------------------------------------
Time per iteration: 0.00511 secs
Time to completion: 0.04 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 40
-----------------------------------------------------------
RHO (Normal): 2.478887852
Acceptance Rate (Normal): 0.3207381371
Parameter RMS: 0.2720625985
Avg. Variance: 0.05147839875
Log-Likelihood: -6397.076152
RLH: 0.5402388242
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.0462136
Price: -0.1733574
-----------------------------------------------------------
Time per iteration: 0.0139 secs
Time to completion: 0.106 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 50
-----------------------------------------------------------
RHO (Normal): 2.357397682
Acceptance Rate (Normal): 0.2855887522
Parameter RMS: 0.2722019479
Avg. Variance: 0.05063214595
Log-Likelihood: -6339.856731
RLH: 0.5439869765
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01953859
Price: -0.21579848
-----------------------------------------------------------
Time per iteration: 0.00483 secs
Time to completion: 0.0362 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 60
-----------------------------------------------------------
RHO (Normal): 2.241861739
Acceptance Rate (Normal): 0.3567662566
Parameter RMS: 0.2764390867
Avg. Variance: 0.06313342568
Log-Likelihood: -6347.651173
RLH: 0.5430444561
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01141959
Price: -0.23790466
-----------------------------------------------------------
Time per iteration: 0.0048 secs
Time to completion: 0.0352 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 70
-----------------------------------------------------------
RHO (Normal): 2.605763364
Acceptance Rate (Normal): 0.3312829525
Parameter RMS: 0.2710969876
Avg. Variance: 0.06143699572
Log-Likelihood: -6362.973162
RLH: 0.5422146586
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.009828258
Price: -0.250698586
-----------------------------------------------------------
Time per iteration: 0.00483 secs
Time to completion: 0.0346 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 80
-----------------------------------------------------------
RHO (Normal): 2.027499572
Acceptance Rate (Normal): 0.2996485062
Parameter RMS: 0.2764993471
Avg. Variance: 0.06769038661
Log-Likelihood: -6325.983248
RLH: 0.5443907577
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.008622545
Price: -0.282523399
-----------------------------------------------------------
Time per iteration: 0.00503 secs
Time to completion: 0.0352 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 90
-----------------------------------------------------------
RHO (Normal): 2.356605679
Acceptance Rate (Normal): 0.3260105448
Parameter RMS: 0.2839082366
Avg. Variance: 0.07329111296
Log-Likelihood: -6285.719778
RLH: 0.5462002534
-----------------------------------------------------------
Random Parameters Estimate
WTP: -0.009063934
Price: -0.319521571
-----------------------------------------------------------
Time per iteration: 0.00477 secs
Time to completion: 0.0326 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 100
-----------------------------------------------------------
RHO (Normal): 2.739132674
Acceptance Rate (Normal): 0.3066783831
Parameter RMS: 0.2938470669
Avg. Variance: 0.08237665634
Log-Likelihood: -6305.936849
RLH: 0.5453471285
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01012956
Price: -0.32946904
-----------------------------------------------------------
Time per iteration: 0.00481 secs
Time to completion: 0.0321 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 110
-----------------------------------------------------------
RHO (Normal): 2.604887919
Acceptance Rate (Normal): 0.295254833
Parameter RMS: 0.2946394543
Avg. Variance: 0.08322545039
Log-Likelihood: -6291.331493
RLH: 0.5461513284
-----------------------------------------------------------
Random Parameters Estimate
WTP: -0.001526503
Price: -0.325496441
-----------------------------------------------------------
Time per iteration: 0.0049 secs
Time to completion: 0.0318 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 120
-----------------------------------------------------------
RHO (Normal): 2.477222492
Acceptance Rate (Normal): 0.2917398946
Parameter RMS: 0.3001366273
Avg. Variance: 0.09002404864
Log-Likelihood: -6312.697449
RLH: 0.5447851977
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.0023286
Price: -0.3501747
-----------------------------------------------------------
Time per iteration: 0.00479 secs
Time to completion: 0.0303 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 130
-----------------------------------------------------------
RHO (Normal): 2.87932815
Acceptance Rate (Normal): 0.3198594025
Parameter RMS: 0.317051085
Avg. Variance: 0.1053465311
Log-Likelihood: -6284.707853
RLH: 0.5463612097
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01375754
Price: -0.38822913
-----------------------------------------------------------
Time per iteration: 0.00505 secs
Time to completion: 0.0311 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 140
-----------------------------------------------------------
RHO (Normal): 3.34670407
Acceptance Rate (Normal): 0.3014059754
Parameter RMS: 0.3195821539
Avg. Variance: 0.1115147892
Log-Likelihood: -6279.501021
RLH: 0.5461415314
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01438638
Price: -0.39086709
-----------------------------------------------------------
Time per iteration: 0.00487 secs
Time to completion: 0.0292 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 150
-----------------------------------------------------------
RHO (Normal): 2.604012767
Acceptance Rate (Normal): 0.2724077329
Parameter RMS: 0.3308794156
Avg. Variance: 0.1208708807
Log-Likelihood: -6284.016778
RLH: 0.5459580514
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03457599
Price: -0.40813379
-----------------------------------------------------------
Time per iteration: 0.00486 secs
Time to completion: 0.0283 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 160
-----------------------------------------------------------
RHO (Normal): 3.026699172
Acceptance Rate (Normal): 0.3031634446
Parameter RMS: 0.323654504
Avg. Variance: 0.1130006151
Log-Likelihood: -6251.300867
RLH: 0.5478097461
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.02113844
Price: -0.39927396
-----------------------------------------------------------
Time per iteration: 0.00485 secs
Time to completion: 0.0275 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 170
-----------------------------------------------------------
RHO (Normal): 2.35502247
Acceptance Rate (Normal): 0.2961335677
Parameter RMS: 0.3293062923
Avg. Variance: 0.1196142668
Log-Likelihood: -6255.468032
RLH: 0.547786205
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.02745202
Price: -0.40345593
-----------------------------------------------------------
Time per iteration: 0.00485 secs
Time to completion: 0.0267 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 180
-----------------------------------------------------------
RHO (Normal): 2.737292477
Acceptance Rate (Normal): 0.3189806678
Parameter RMS: 0.3356223851
Avg. Variance: 0.1240324656
Log-Likelihood: -6250.325365
RLH: 0.5480194497
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.02135741
Price: -0.41179847
-----------------------------------------------------------
Time per iteration: 0.00493 secs
Time to completion: 0.0263 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 190
-----------------------------------------------------------
RHO (Normal): 2.60313791
Acceptance Rate (Normal): 0.3391915641
Parameter RMS: 0.3343096851
Avg. Variance: 0.1211071643
Log-Likelihood: -6278.892705
RLH: 0.5466303187
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.0158434
Price: -0.4136840
-----------------------------------------------------------
Time per iteration: 0.0138 secs
Time to completion: 0.0713 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 200
-----------------------------------------------------------
RHO (Normal): 2.475558251
Acceptance Rate (Normal): 0.2987697715
Parameter RMS: 0.3433928396
Avg. Variance: 0.1269764728
Log-Likelihood: -6270.992243
RLH: 0.5470646818
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01557675
Price: -0.40061774
-----------------------------------------------------------
Time per iteration: 0.00479 secs
Time to completion: 0.0239 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 210
-----------------------------------------------------------
RHO (Normal): 2.877393767
Acceptance Rate (Normal): 0.3040421793
Parameter RMS: 0.3465950065
Avg. Variance: 0.1307444441
Log-Likelihood: -6267.266255
RLH: 0.547053059
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.01573064
Price: -0.40481985
-----------------------------------------------------------
Time per iteration: 0.00483 secs
Time to completion: 0.0233 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 220
-----------------------------------------------------------
RHO (Normal): 2.736372842
Acceptance Rate (Normal): 0.3057996485
Parameter RMS: 0.3587176313
Avg. Variance: 0.1436690142
Log-Likelihood: -6202.197798
RLH: 0.5508132206
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03151904
Price: -0.42015661
-----------------------------------------------------------
Time per iteration: 0.00495 secs
Time to completion: 0.0231 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 230
-----------------------------------------------------------
RHO (Normal): 2.602263346
Acceptance Rate (Normal): 0.2794376098
Parameter RMS: 0.3874735134
Avg. Variance: 0.1680813896
Log-Likelihood: -6209.863932
RLH: 0.5505157645
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.02550019
Price: -0.47043068
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.022 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 240
-----------------------------------------------------------
RHO (Normal): 2.474726549
Acceptance Rate (Normal): 0.3189806678
Parameter RMS: 0.3776896113
Avg. Variance: 0.1596189741
Log-Likelihood: -6222.284227
RLH: 0.5498800404
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03578634
Price: -0.45992533
-----------------------------------------------------------
Time per iteration: 0.00489 secs
Time to completion: 0.0212 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 250
-----------------------------------------------------------
RHO (Normal): 2.353440325
Acceptance Rate (Normal): 0.2741652021
Parameter RMS: 0.3636392058
Avg. Variance: 0.1493022531
Log-Likelihood: -6242.442354
RLH: 0.5487430808
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03329289
Price: -0.43999711
-----------------------------------------------------------
Time per iteration: 0.00477 secs
Time to completion: 0.0199 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 260
-----------------------------------------------------------
RHO (Normal): 2.735453516
Acceptance Rate (Normal): 0.2688927944
Parameter RMS: 0.3705459799
Avg. Variance: 0.1559512501
Log-Likelihood: -6235.561288
RLH: 0.5486691149
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03339947
Price: -0.45816968
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.0195 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 270
-----------------------------------------------------------
RHO (Normal): 2.601389076
Acceptance Rate (Normal): 0.2855887522
Parameter RMS: 0.3849031848
Avg. Variance: 0.1630008291
Log-Likelihood: -6228.984457
RLH: 0.5496331684
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.02760512
Price: -0.47367304
-----------------------------------------------------------
Time per iteration: 0.00484 secs
Time to completion: 0.0185 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 280
-----------------------------------------------------------
RHO (Normal): 3.0236496
Acceptance Rate (Normal): 0.3057996485
Parameter RMS: 0.3947922074
Avg. Variance: 0.1744267078
Log-Likelihood: -6249.033566
RLH: 0.5483138937
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03317348
Price: -0.47609350
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.0179 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 290
-----------------------------------------------------------
RHO (Normal): 2.352649651
Acceptance Rate (Normal): 0.2943760984
Parameter RMS: 0.3967730381
Avg. Variance: 0.1755300487
Log-Likelihood: -6238.288487
RLH: 0.5491907592
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03517681
Price: -0.47475612
-----------------------------------------------------------
Time per iteration: 0.00498 secs
Time to completion: 0.0174 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 300
-----------------------------------------------------------
RHO (Normal): 2.734534499
Acceptance Rate (Normal): 0.309314587
Parameter RMS: 0.396286579
Avg. Variance: 0.178924374
Log-Likelihood: -6241.989956
RLH: 0.5486498317
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04380939
Price: -0.45858404
-----------------------------------------------------------
Time per iteration: 0.00481 secs
Time to completion: 0.016 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 310
-----------------------------------------------------------
RHO (Normal): 2.6005151
Acceptance Rate (Normal): 0.2776801406
Parameter RMS: 0.4005202601
Avg. Variance: 0.1826253697
Log-Likelihood: -6221.174193
RLH: 0.5500535593
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04619759
Price: -0.50043058
-----------------------------------------------------------
Time per iteration: 0.00494 secs
Time to completion: 0.0157 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 320
-----------------------------------------------------------
RHO (Normal): 2.473063985
Acceptance Rate (Normal): 0.295254833
Parameter RMS: 0.4026059938
Avg. Variance: 0.1840046035
Log-Likelihood: -6207.475939
RLH: 0.550838876
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04578772
Price: -0.49049084
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.0147 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 330
-----------------------------------------------------------
RHO (Normal): 2.874494629
Acceptance Rate (Normal): 0.3145869947
Parameter RMS: 0.3903394667
Avg. Variance: 0.1701092072
Log-Likelihood: -6211.49385
RLH: 0.5508800074
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04043269
Price: -0.47824114
-----------------------------------------------------------
Time per iteration: 0.00489 secs
Time to completion: 0.0139 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 340
-----------------------------------------------------------
RHO (Normal): 2.236594738
Acceptance Rate (Normal): 0.2943760984
Parameter RMS: 0.3916609956
Avg. Variance: 0.1721631282
Log-Likelihood: -6203.357388
RLH: 0.5509781514
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04685106
Price: -0.48457618
-----------------------------------------------------------
Time per iteration: 0.00492 secs
Time to completion: 0.0131 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 350
-----------------------------------------------------------
RHO (Normal): 2.599641418
Acceptance Rate (Normal): 0.2891036907
Parameter RMS: 0.3876331996
Avg. Variance: 0.1670445092
Log-Likelihood: -6178.188181
RLH: 0.5521206664
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.03520622
Price: -0.46867893
-----------------------------------------------------------
Time per iteration: 0.0135 secs
Time to completion: 0.0338 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 360
-----------------------------------------------------------
RHO (Normal): 2.472233121
Acceptance Rate (Normal): 0.2891036907
Parameter RMS: 0.3974743256
Avg. Variance: 0.1812562915
Log-Likelihood: -6237.433884
RLH: 0.5488422421
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04847559
Price: -0.48805959
-----------------------------------------------------------
Time per iteration: 0.00481 secs
Time to completion: 0.0112 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 370
-----------------------------------------------------------
RHO (Normal): 2.3510691
Acceptance Rate (Normal): 0.2891036907
Parameter RMS: 0.4016339987
Avg. Variance: 0.1854971898
Log-Likelihood: -6239.960169
RLH: 0.549140605
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04257693
Price: -0.49265862
-----------------------------------------------------------
Time per iteration: 0.00477 secs
Time to completion: 0.0103 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 380
-----------------------------------------------------------
RHO (Normal): 2.732697391
Acceptance Rate (Normal): 0.30228471
Parameter RMS: 0.4100367937
Avg. Variance: 0.1962747582
Log-Likelihood: -6230.07327
RLH: 0.5491135704
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05405504
Price: -0.50787303
-----------------------------------------------------------
Time per iteration: 0.00498 secs
Time to completion: 0.00996 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 390
-----------------------------------------------------------
RHO (Normal): 2.598768029
Acceptance Rate (Normal): 0.2873462214
Parameter RMS: 0.417165855
Avg. Variance: 0.2020739328
Log-Likelihood: -6182.791457
RLH: 0.5519658415
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04811652
Price: -0.51914157
-----------------------------------------------------------
Time per iteration: 0.0052 secs
Time to completion: 0.00953 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 400
-----------------------------------------------------------
RHO (Normal): 2.471402537
Acceptance Rate (Normal): 0.2811950791
Parameter RMS: 0.4165320641
Avg. Variance: 0.203120914
Log-Likelihood: -6200.198157
RLH: 0.5507549761
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04161142
Price: -0.53561482
-----------------------------------------------------------
Time per iteration: 0.00493 secs
Time to completion: 0.00822 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 410
-----------------------------------------------------------
RHO (Normal): 2.872563494
Acceptance Rate (Normal): 0.3075571178
Parameter RMS: 0.407394919
Avg. Variance: 0.1936872594
Log-Likelihood: -6237.696447
RLH: 0.548901719
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05279738
Price: -0.52214365
-----------------------------------------------------------
Time per iteration: 0.00482 secs
Time to completion: 0.00723 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 420
-----------------------------------------------------------
RHO (Normal): 2.235092155
Acceptance Rate (Normal): 0.2987697715
Parameter RMS: 0.4166975822
Avg. Variance: 0.2026367784
Log-Likelihood: -6211.456375
RLH: 0.5504695076
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04844027
Price: -0.53422111
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.00651 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 430
-----------------------------------------------------------
RHO (Normal): 2.597894933
Acceptance Rate (Normal): 0.3101933216
Parameter RMS: 0.4130540822
Avg. Variance: 0.1968258702
Log-Likelihood: -6211.278103
RLH: 0.5506168281
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.04932911
Price: -0.52620975
-----------------------------------------------------------
Time per iteration: 0.00486 secs
Time to completion: 0.00567 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 440
-----------------------------------------------------------
RHO (Normal): 3.019588284
Acceptance Rate (Normal): 0.3084358524
Parameter RMS: 0.4193359481
Avg. Variance: 0.2049347772
Log-Likelihood: -6215.13207
RLH: 0.5506200561
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05515558
Price: -0.51345618
-----------------------------------------------------------
Time per iteration: 0.00484 secs
Time to completion: 0.00484 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 450
-----------------------------------------------------------
RHO (Normal): 2.871598413
Acceptance Rate (Normal): 0.3040421793
Parameter RMS: 0.4236825038
Avg. Variance: 0.207800636
Log-Likelihood: -6219.87991
RLH: 0.5499500632
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.0526718
Price: -0.5310368
-----------------------------------------------------------
Time per iteration: 0.0049 secs
Time to completion: 0.00408 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 460
-----------------------------------------------------------
RHO (Normal): 2.730861518
Acceptance Rate (Normal): 0.3057996485
Parameter RMS: 0.4148841118
Avg. Variance: 0.2024618865
Log-Likelihood: -6205.166952
RLH: 0.5508063027
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05368845
Price: -0.51361749
-----------------------------------------------------------
Time per iteration: 0.00485 secs
Time to completion: 0.00323 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 470
-----------------------------------------------------------
RHO (Normal): 2.597022131
Acceptance Rate (Normal): 0.3268892794
Parameter RMS: 0.4182879148
Avg. Variance: 0.2016471529
Log-Likelihood: -6198.583489
RLH: 0.5512758293
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05611717
Price: -0.53006742
-----------------------------------------------------------
Time per iteration: 0.00488 secs
Time to completion: 0.00244 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 480
-----------------------------------------------------------
RHO (Normal): 2.469742206
Acceptance Rate (Normal): 0.309314587
Parameter RMS: 0.4196575616
Avg. Variance: 0.2069126384
Log-Likelihood: -6185.995692
RLH: 0.5519201977
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05772128
Price: -0.52757466
-----------------------------------------------------------
Time per iteration: 0.0049 secs
Time to completion: 0.00163 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 490
-----------------------------------------------------------
RHO (Normal): 2.348700264
Acceptance Rate (Normal): 0.2811950791
Parameter RMS: 0.4219524381
Avg. Variance: 0.2122793557
Log-Likelihood: -6191.760395
RLH: 0.5514095925
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.06871362
Price: -0.53411055
-----------------------------------------------------------
Time per iteration: 0.0136 secs
Time to completion: 0.00226 mins
-----------------------------------------------------------
-----------------------------------------------------------
Iteration: 500
-----------------------------------------------------------
RHO (Normal): 2.729944043
Acceptance Rate (Normal): 0.3145869947
Parameter RMS: 0.4156325427
Avg. Variance: 0.2011661706
Log-Likelihood: -6213.70571
RLH: 0.5503714364
-----------------------------------------------------------
Random Parameters Estimate
WTP: 0.05525883
Price: -0.52521068
-----------------------------------------------------------
Time per iteration: 0.00482 secs
Time to completion: 0 mins
-----------------------------------------------------------
Estimation complete.
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