# ProbitRE_PLNRE: Poisson Lognormal Model with Random Effects and Sample... In PanelCount: Random Effects and/or Sample Selection Models for Panel Count Data

 ProbitRE_PLNRE R Documentation

## Poisson Lognormal Model with Random Effects and Sample Selection

### Description

Estimates the following two-stage model:

Selection equation (ProbitRE - Probit model with individual level random effects):

z_{it}=1(\boldsymbol{\alpha}\mathbf{w_{it}}'+\delta u_i+\xi_{it} > 0)

Outcome Equation (PLN_RE - Poisson Lognormal model with individual-time level random effects):

E[y_{it}|x_{it},v_i,\epsilon_{it}] = exp(\boldsymbol{\beta}\mathbf{x_{it}}' + \sigma v_i + \gamma \epsilon_{it})

Correlation (self-selection at both individual and individual-time level):

• u_i and v_i are bivariate normally distributed with a correlation of \rho.

• \xi_{it} and \epsilon_{it} are bivariate normally distributed with a correlation of \tau.

Notations:

• w_{it}: variables influencing the selection decision z_{it}, which could be a mixture of time-variant variables, time-invariant variables, and time dummies

• x_{it}: variables influencing the outcome y_{it}, which could be a mixture of time-variant variables, time-invariant variables, and time dummies

• u_i: individual level random effect in the selection equation

• v_i: individual level random effect in the outcome equation

• \xi_{it}: error term in the selection equation

• \epsilon_{it}: individual-time level random effect in the outcome equation

### Usage

ProbitRE_PLNRE(
sel_form,
out_form,
data,
id.name,
testData = NULL,
par = NULL,
disable_rho = FALSE,
disable_tau = FALSE,
delta = NULL,
sigma = NULL,
gamma = NULL,
rho = NULL,
tau = NULL,
method = "BFGS",
se_type = c("BHHH", "Hessian")[1],
H = c(10, 10),
psnH = 20,
prbH = 20,
plnreH = 20,

### Value

A list containing the results of the estimated model, some of which are inherited from the return of optim

• estimates: Model estimates with 95% confidence intervals

• par: Point estimates

• var_bhhh: BHHH covariance matrix, inverse of the outer product of gradient at the maximum

• se_bhhh: BHHH standard errors

• g: Gradient function at maximum

• gtHg: g'H^-1g, where H^-1 is approximated by var_bhhh. A value close to zero (e.g., <1e-3 or 1e-6) indicates good convergence.

• LL: Likelihood

• AIC: AIC

• BIC: BIC

• n_obs: Number of observations

• time: Time takes to estimate the model

• partial: Average partial effect at the population level

• paritalAvgObs: Partial effect for an individual with average characteristics

• predict: A list with predicted participation probability (prob), predicted potential outcome (outcome), and predicted actual outcome (actual_outcome).

• counts: From optim. A two-element integer vector giving the number of calls to fn and gr respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.

• message: From optim. A character string giving any additional information returned by the optimizer, or NULL.

• convergence: From optim. An integer code. 0 indicates successful completion. Note that the list inherits all the complements in the output of optim. See the documentation of optim for more details.

### References

1. Peng, J., & Van den Bulte, C. (2023). Participation vs. Effectiveness in Sponsored Tweet Campaigns: A Quality-Quantity Conundrum. Management Science (forthcoming). Available at SSRN: https://www.ssrn.com/abstract=2702053

2. Peng, J., & Van den Bulte, C. (2015). How to Better Target and Incent Paid Endorsers in Social Advertising Campaigns: A Field Experiment. 2015 International Conference on Information Systems. https://aisel.aisnet.org/icis2015/proceedings/SocialMedia/24/

Other PanelCount: PLN_RE(), PoissonRE(), ProbitRE_PoissonRE(), ProbitRE()

### Examples


# Use the simulated dataset, in which the true coefficients of x and w are 1 in both stages.
# The model can recover the true parameters very well
data(sim)
res = ProbitRE_PLNRE(z~x+w, y~x, data=sim, id.name='id')
res\$estimates



PanelCount documentation built on Aug. 21, 2023, 9:09 a.m.