nmm: Maximum likelihood estimation of nonlinear multivariate...
In nmm: Nonlinear Multivariate Models

Description Usage Arguments Value Examples

nmm, nmm_sigma and summary are the main functions used for the estimation of NMM.

nmm - Maximum likelihood estimation of nonlinear multivariate models (NMM)
nmm_sigma - Optimizes the covariance matrix
summary - returns summary of nmm object with "normal", "robust" or "clustered" standard errors. With option new_coef one can supply new coefficients and test their significance.

nmm(
  data,
  eq_type = c("joint", "cont", "disc"),
  eq_d = NULL,
  eq_c = NULL,
  par_c = NULL,
  par_d = NULL,
  start_v = NULL,
  check_hess = TRUE,
  corrl = TRUE,
  weight_paths = TRUE,
  weight_paths_cont = FALSE,
  data_weight = NULL,
  estimate = TRUE,
  fixed_term = FALSE,
  best_method = FALSE,
  DEoptim_run = FALSE,
  hessian = "joint_hess",
  print_out = FALSE,
  diff_hessian = FALSE,
  bayesian_random = FALSE,
  DEoptim_run_main = FALSE,
  deconst = 2,
  numerical_deriv = FALSE,
  best_method4start = FALSE,
  eqsys = "sur",
  miterlim = 10000,
  opt_method = "BFGS",
  try_last_DEoptim = TRUE,
  transform = NULL,
  MNtypef = "logit",
  nmm_object = NULL
)

## S3 method for class 'nmm'
summary(object, type = "normal", new_coef = NULL, ...)

nmm_sigma(
  object,
  methodopt = "BFGS",
  try_1good = TRUE,
  try_DEoptim = FALSE,
  try_diff_method = FALSE,
  trace = FALSE,
  estimate = FALSE
)

`data`	`data.frame` used in the optimization.
`eq_type`	Possible options "joint", "cont", "disc".
`eq_d`	Discrete equations.
`eq_c`	Continuous equations.
`par_c`	Parameters from continuous equations.
`par_d`	Parameters from discrete equations.
`start_v`	Starting values for optimization. If `NULL`, starting values are found by `get_start` function.
`check_hess`	If `TRUE`, check the Hessian.
`corrl`	If `TRUE`, correlation between blocks (continuous and discrete).
`weight_paths`	If `TRUE`, weight according to the number of choices made by individual i will be added to the whole system.
`weight_paths_cont`	If `TRUE`, if only to continuous part should be weighted.
`data_weight`	Data weight matrix.
`estimate`	If `TRUE`, estimation is performed.
`fixed_term`	If `TRUE`, includes fixed term to continuous equation block.
`best_method`	If `TRUE`, all optimizers are checked.
`DEoptim_run`	If `TRUE`, runs `DEoptim` in generation of starting values.
`hessian`	String, name of the Hessian function.
`print_out`	If `TRUE`, prints out log-likelihood for each equation.
`diff_hessian`	If `TRUE`, for changing hessian and gradient with weights.
`bayesian_random`	If `TRUE`, than par[1] is changed to par[,1] to be used for optimization of random parameters in Bayesian estimation.
`DEoptim_run_main`	If `TRUE`, run `DEoptim` in the main optimization.
`deconst`	absolute value of lower and upper bound in `DEoptim` optimization.
`numerical_deriv`	If `TRUE`, uses numerical derivative instead of the analytical.
`best_method4start`	If `TRUE`, all optimizers are checked for starting values.
`eqsys`	"sur" or "sem".
`miterlim`	Number many iterations passed to `maxLik` function
`opt_method`	optimization method for `maxLik`.
`try_last_DEoptim`	If `TRUE`, in case of error in `maxLik` should `DEoptim` be run.
`transform`	if `TRUE`, quantile transformation is applied to discrete equations.
`MNtypef`	estimate "logit", or "dogit"
`nmm_object`	`nmm` object created by `nmm` function.
`object`	`nmm` object, for `summary` and `nmm_sigma`
`type`	Type of standard errors c("robust", "clustered", "normal"), for `summary`
`new_coef`	New coefficients that will be tested, for `summary`
`...`	additional arguments affecting the summary produced, for `summary`
`methodopt`	optimizer from `maxLik` package, for `nmm_sigma`
`try_1good`	If `TRUE`, stops then first good values are found, for `nmm_sigma`
`try_DEoptim`	If `TRUE`, uses `DEoptim` for optimization, then `maxLik` optimizers produce errors, for `nmm_sigma`
`try_diff_method`	If `TRUE`, stops then first good values with Hessian check are found, for `nmm_sigma`
`trace`	If `TRUE`, trace of `DEoptim` is printed, for `nmm_sigma`

`nmm`	returns `nmm` object with estimated parameters, functions, and data.
`nmm_sigma`	returns estimated parameters, functions, data.
`summary`	returns summary of `nmm` object.

# estimation of System of Nonlinear Equations based on example from 'systemfit'
library(systemfit)
data( ppine , package="systemfit")
hg.formula <- hg ~ exp( h0 + h1*log(tht) + h2*tht^2 + h3*elev)
dg.formula <- dg ~ exp( d0 + d1*log(dbh) + d2*hg + d3*cr)
labels <- list( "height.growth", "diameter.growth" )
model <- list( hg.formula, dg.formula )
start.values <- c(h0=-0.5, h1=0.5, h2=-0.001, h3=0.0001,
                  d0=-0.5, d1=0.009, d2=0.25, d3=0.005)
model.sur <- nlsystemfit( "SUR", model, start.values, data=ppine, eqnlabels=labels )
eq_c <- as.character(c(hg.formula, dg.formula))
parl <- c(paste0("h", 0:3),paste0("d", 0:3))
res <- nmm(ppine, eq_c=eq_c, par_c=parl, start_v = start.values,
eq_type = "cont", best_method = FALSE, numerical_deriv=TRUE)
summary(res)
res_sigma_cont <- nmm_sigma(res,estimate=TRUE) # Estimation of the Variance-Covariance matrix
summary(res_sigma_cont)

#example discrete choice
library(mlogit)
data("Fishing", package = "mlogit")
Fish <- mlogit.data(Fishing, varying = c(2:9), shape = "wide", choice = "mode")
## a pure "conditional" model
mres <- summary(mlogit(mode ~ price + catch, data = Fish))
data <- prepare_data(Fish %>% data.frame %>% dplyr::select(-idx),
choice="alt", dummy="mode", PeID="chid", mode_spec_var = c("price", "catch"),
 type="long")
eq_d <- c("a1 + p1 * price_1 + p2 * catch_2", "a2 + p1 * price_2 + p2 * catch_2",
             "a3 + p1 * price_3 + p2 * catch_3", "a4 + p1 * price_4 + p2 * catch_4")
par_d <- c(paste0("a", 1:4), paste0("p", 1:2))
res <- nmm(data, eq_d=eq_d, par_d = par_d,  eq_type="disc", fixed_term=FALSE,
best_method=FALSE)
summary(res)

# joint estimation mockup example
data(dataM)
dataMp <- dataM %>% data.frame %>% prepare_data(. , choice="DR_Course", 
PeID = "Student")
eq_c <- c("PlcmtScore ~ exp(a0 + a1 * PSATM + a2 * Rank + a3 * Size)",
"ACTM ~ exp(c0 + c1 * GPAadj)")
par_c <- c(paste0("a", 0:3), paste0("c", 0:1))
eq_d <- c("ASC1" ,
"ASC2 + b1_2 * SATM + b2_2 * PlcmtScore",
"ASC3 + b1_3 * SATM + b2_3 * PlcmtScore")
par_d <- c(paste0("ASC", 1:3), paste0("b", rep(1:2, rep(2,2)), "_", 2:3))

nmm_joint_res <- nmm(dataMp, eq_type = "joint", eq_d = eq_d, 
par_d = par_d,  eq_c = eq_c, par_c = par_c, 
start_v = c(a0=3.394, a1=0.001, a2=-0.001, a3=0, c0=3.583, c1=-0.008, 
ASC2=-1.452, ASC3=3.047, b1_2=0.145, b1_3=0.102, b2_2=-0.133, b2_3=-0.168))
summary(nmm_joint_res)