Random Parameters Count Regression Models
countreg.rp.RdRandom Parameters Count Regression Models
Usage
countreg.rp(
formula,
rpar_formula,
data,
family = "NB2",
rpardists = NULL,
dis_param_formula_1 = NULL,
dis_param_formula_2 = NULL,
het_mean_formula = NULL,
het_var_formula = NULL,
ndraws = 500,
scrambled = FALSE,
correlated = FALSE,
panel_id = NULL,
weights = NULL,
offset = NULL,
method = "BHHH",
max.iters = 1000,
start.vals = NULL,
verbose = FALSE
)Arguments
- formula
an R formula. This formula should specify the outcome and the independent variables that have fixed parameters.
- rpar_formula
a symbolic description of the model related specifically to the random parameters. This should not include an outcome variable. If the intercept is random, include it in this formula. If the intercept is fixed, include it in
formulabut not inrpar_formula.- data
a dataframe that has all of the variables in the
formulaandrpar_formula.- family
the name of the distribution/model type to estimate. Default is "NB2". Options include "Poisson", "NB1", "NB2", "NBP", "PIG", "Sichel", etc. (See
countregfor full list).- rpardists
an optional named vector whose names are the random parameters and values the distribution. The distribution options include normal ("n"), lognormal ("ln"), triangular ("t"), uniform ("u"), and gamma ("g"). If not provided, normal is used.
- dis_param_formula_1
a symbolic description of the model for the first parameter of the count distribution (e.g., ln(alpha) for NB2).
- dis_param_formula_2
a symbolic description of the model for the second parameter of the count distribution (if applicable).
- het_mean_formula
an optional symbolic description of the model for heterogeneity in the means of the random parameters.
- het_var_formula
an optional symbolic description of the model for heterogeneity in the variances of the random parameters.
- ndraws
the number of Halton draws to use for estimating the random parameters.
- scrambled
if the Halton draws should be scrambled.
if the random parameters should be correlated. If TRUE, only normal distributions are used.
- panel_id
an optional variable name (string) or vector defining the panel structure (repeated measures). If provided, the standard errors and likelihood are estimated accounting for the panel structure.
- weights
variable name to be used as frequency weights.
- offset
variable name to be used as an offset.
- method
optimization method (e.g., "BHHH", "BFGS", "NM").
- max.iters
maximum number of iterations.
- start.vals
optional vector of starting values.
- verbose
logical.
Value
An object of class `countreg` which is a list with the following components:
model: the fitted model object.
data: the data frame used to fit the model.
call: the matched call.
formula: the formula used to fit the model.
Examples
# \donttest{
# Load data
data("washington_roads")
washington_roads$AADT10kplus <- ifelse(washington_roads$AADT > 10000, 1, 0)
# 1. Basic Random Parameters Negative Binomial (NB2)
rp_nb2 <- countreg.rp(Total_crashes ~ lnaadt + lnlength,
rpar_formula = ~ -1 + speed50,
data = washington_roads,
family = "NB2",
rpardists = c(speed50 = "n"),
ndraws = 100,
method = "BHHH")
summary(rp_nb2)
#> Call:
#> Total_crashes ~ lnaadt + lnlength
#>
#> Method: countreg.rp
#> Iterations: 28
#> Convergence: successive function values within relative tolerance limit (reltol)
#> Log-likelihood: -1082.98
#>
#> Parameter Estimates:
#> # A tibble: 6 × 7
#> parameter coeff `Std. Err.` `t-stat` `p-value` `lower CI` `upper CI`
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) -8.76 0.044 -199. 0 -8.84 -8.67
#> 2 lnaadt 1.08 0.005 213. 0 1.07 1.09
#> 3 lnlength 0.756 0.035 21.7 0 0.688 0.825
#> 4 speed50:Mean -0.744 0.106 -7.04 0 -0.951 -0.537
#> 5 speed50:St.Dev 0.715 0.177 4.04 0 0.368 1.06
#> 6 ln(alpha) -1.32 0.293 -4.5 0 -1.89 -0.744
# 2. Random Parameters with Panel Structure (if 'site_id' exists)
# rp_panel <- countreg.rp(Total_crashes ~ -1 + lnaadt,
# rpar_formula = ~ speed50,
# data = washington_roads,
# panel_id = "site_id",
# family = "NB2",
# ndraws = 100)
# 3. Generalized Random Parameters Model with Heterogeneity
rp_gen <- countreg.rp(Total_crashes ~ lnaadt,
rpar_formula = ~ -1 + speed50,
dis_param_formula_1 = ~ lnlength,
het_mean_formula = ~ AADT10kplus,
data = washington_roads,
family = "NB2",
rpardists = c(speed50 = "n"),
ndraws = 100)
summary(rp_gen)
#> Call:
#> Total_crashes ~ lnaadt
#>
#> Method: countreg.rp
#> Iterations: 11
#> Convergence: successive function values within relative tolerance limit (reltol)
#> Log-likelihood: -1140.142
#>
#> Parameter Estimates:
#> # A tibble: 7 × 7
#> parameter coeff `Std. Err.` `t-stat` `p-value` `lower CI` `upper CI`
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) -8.54 4.7 e-2 -182. 0 -8.64e+0 -8.45e+0
#> 2 lnaadt 0.965 6 e-3 174. 0 9.54e-1 9.76e-1
#> 3 speed50:Mean -0.834 1.15e-1 -7.28 0 -1.06e+0 -6.1 e-1
#> 4 speed50:St.Dev 0.83 1.52e-1 5.46 0 5.32e-1 1.13e+0
#> 5 HetMean:AADT10kp… -18.4 7.41e+7 0 1 -1.45e+8 1.45e+8
#> 6 ln(alpha):(Inter… -1.21 1.92e-1 -6.29 0 -1.58e+0 -8.31e-1
#> 7 ln(alpha):lnleng… -0.49 1.45e-1 -3.38 0.001 -7.74e-1 -2.06e-1
# 4. Random Parameters Poisson Model with panel specification
rp_poisson <- countreg.rp(Total_crashes ~ lnaadt,
rpar_formula = ~ -1 + speed50,
dis_param_formula_1 = ~ lnlength,
het_mean_formula = ~ AADT10kplus,
data = washington_roads,
family = "POISSON",
rpardists = c(speed50 = "n"),
ndraws = 100,
panel_id = "ID")
summary(rp_poisson)
#> Call:
#> Total_crashes ~ lnaadt
#>
#> Method: countreg.rp
#> Iterations: 14
#> Convergence: successive function values within relative tolerance limit (reltol)
#> Log-likelihood: -1161.137
#>
#> Parameter Estimates:
#> # A tibble: 5 × 7
#> parameter coeff `Std. Err.` `t-stat` `p-value` `lower CI` `upper CI`
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) -8.66 0.025 -342. 0 -8.71 -8.61
#> 2 lnaadt 0.974 0.003 342. 0 0.968 0.98
#> 3 speed50:Mean -0.838 0.124 -6.74 0 -1.08 -0.594
#> 4 speed50:St.Dev 0.869 0.151 5.76 0 0.574 1.16
#> 5 HetMean:AADT10k… -110. NA NA NA NA NA
# }