Produces coefficient tables for the regression and for the copula dependence parameters, the likelihood-ratio and bootstrap Wald tests of no endogeneity, fit statistics, and the identification diagnostics.
Arguments
- object
A fitted
"copregpanel"object.- ...
Currently unused.
- x
An object of class
"summary.copregpanel", as returned bysummary.copregpanel.- digits
Number of significant digits to print.
- signif.stars
Logical; show significance stars, as in
printCoefmat.
Value
An object of class "summary.copregpanel", a list
including
- coefficients
a coefficient table (estimate, bootstrap standard error, z value, p value) for the regression
- rho
the equivalent table for the copula correlation(s) and
sigma2- lr.test, wald.test
the likelihood-ratio and bootstrap Wald tests of
rho = 0- r.squared
transformed, structural, within, between and overall R-squared
and further elements carried over from the fitted object, such as
logLik, AIC, BIC and diagnostics.
x, invisibly.
Examples
# \donttest{
set.seed(1)
N <- 30L; Time <- 6L
d <- data.frame(id = rep(seq_len(N), each = Time),
year = rep(seq_len(Time), times = N))
alpha <- rep(rnorm(N), each = Time)
e <- rnorm(N * Time)
d$x <- exp(rnorm(N * Time) + 0.5 * e) # endogenous: correlated with e
d$z <- rnorm(N * Time) # exogenous
d$y <- alpha + 0.5 * d$x + d$z + e
fit <- CopRegPANEL(y ~ x | z, data = d, index = c("id", "year"),
nboots = 15, verbose = FALSE)
summary(fit)
#>
#> Panel copula MLE (Haschka 2022)
#>
#> Call:
#> CopRegPANEL(formula = y ~ x | z, data = d, index = c("id", "year"),
#> nboots = 15, verbose = FALSE)
#>
#> Panel: index = (id, year)
#> 30 cross-sectional units, T = 6
#> 180 observations, 150 after the forward orthogonal deviations transformation
#> no constant in the transformed regression: the structural intercept is
#> time invariant and goes with the individual effects
#>
#> Residuals of the structural model (y - alpha_i - x'beta - z'delta):
#> Min 1Q Median 3Q Max
#> -2.64558 -0.63148 -0.07251 0.50013 2.47346
#>
#> Residuals of the transformed model, which the likelihood treats as normal:
#> Min 1Q Median 3Q Max
#> -2.89808 -0.56351 0.01295 0.78300 2.61122
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> x 0.47548 0.07064 6.731 1.69e-11 ***
#> z 0.94479 0.12728 7.423 1.14e-13 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Dependence parameters: rho(P*, xi*) is the correlation between the normal
#> score of an endogenous regressor and that of the error, and sigma^2 is the
#> variance of the error of the transformed model. rho = 0 means no endogeneity.
#> Estimate Std. Error z value Pr(>|z|)
#> rho(x*, xi*) 0.4469 0.1502 2.975 0.00293 **
#> sigma2 0.9559 0.1245
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> No endogeneity, all rho = 0:
#> likelihood ratio chi-squared = 6.277 on 1 df, p = 0.01223
#> bootstrap Wald chi-squared = 8.849 on 1 df, p = 0.002933
#>
#> R-squared:
#> transformed model 0.762 structural model 0.828
#> within 0.783 between 0.3704 overall 0.6684
#> within, between and overall are squared correlations excluding the
#> individual effects.
#>
#> Log-likelihood -192.7 on 4 parameters; AIC 393.4, BIC 405.4
#> Standard errors from 15 panel bootstrap replicates (cross-sectional units
#> resampled, not rows); cdf = "kde.plugin", ties = "max"; optimiser BFGS.
#> Pr(>|z|) in both tables: Wald test using the normal approximation with
#> the bootstrap standard error.
#>
#> --- Identification diagnostics ------------------------------------
#>
#> Non-normality of the transformed endogenous regressors
#> (small p = non-normal, which is what identifies the model):
#> AD AD p KS p
#> x 7.074 2.193e-17 0.0008258
#>
#> Collinearity of the copula data (omega near 0 = weakly identified):
#> corr(P, C) omega
#> x 0.9094 0.182
#>
# }