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chantrics adjusts the loglikelihood of common
econometric models for clustered data based on the estimation process
suggested in Chandler and Bate (2007), using the chandwich
package, and provides convenience functions for inference on the
adjusted models. adj_loglik() adjusts the parameter
covariance matrix of the models to incorporate clustered data, and can
mitigate model misspecification by wrapping
chandwich::adjust_loglik for the supported models.
The returned model of class chantrics can be plugged
into standard model evaluation and model comparison methods, for example
summary(), confint() and anova(),
and a hypothesis test framework provided by alrtest().
You can install the released version of chantrics from CRAN with:
install.packages("chantrics")The development version is available from GitHub with:
## Remove the # if "devtools" is not installed yet.
# install.packages("devtools")
devtools::install_github("tbruckbauer/chantrics")This example is using the misspecified count data regression from Chapter 5.1 in the Object-Oriented Computation of Sandwich Estimators vignette from the sandwich package (Zeileis 2006). First, data from a negative binomial model is generated, and then a Poisson model is fit, which is clearly misspecified.
library(chantrics)
set.seed(123)
x <- rnorm(250)
y <- rnbinom(250, mu = exp(1 + x), size = 1)
## Fit the Poisson glm model, which is not correctly specified
fm_pois <- glm(y ~ x + I(x ^ 2), family = poisson)
lmtest::coeftest(fm_pois)
#>
#> z test of coefficients:
#>
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 1.063268 0.041357 25.7094 < 2e-16 ***
#> x 0.996072 0.053534 18.6062 < 2e-16 ***
#> I(x^2) -0.049124 0.023146 -2.1223 0.03381 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# The I(x^2) term is spuriously significant.In order to mitigate the misspecification, the loglikelihood
adjustment is applied to the model object using
adj_loglik(model_object). If clustered data is available, a
vector or factor indicating from which cluster the observation
originates can be passed into the function using cluster.
If it is not supplied, it is assumed that each observation originates
from its own cluster and is independent. More information on this can be
found in the clustering
vignette.
## Apply the loglikelihood adjustment to the model
fm_pois_adj <- adj_loglik(fm_pois)
summary(fm_pois_adj)
#> MLE SE adj. SE
#> (Intercept) 1.06300 0.04136 0.08378
#> x 0.99610 0.05353 0.10520
#> I(x^2) -0.04912 0.02315 0.03628
lmtest::coeftest(fm_pois_adj)
#>
#> z test of coefficients:
#>
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 1.063268 0.083776 12.6918 <2e-16 ***
#> x 0.996072 0.105217 9.4668 <2e-16 ***
#> I(x^2) -0.049124 0.036284 -1.3539 0.1758
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# The I(x^2) term is no longer significant.
# Produce confidence intervals for the parameter estimates
chandwich::conf_intervals(fm_pois_adj)
#> Waiting for profiling to be done...
#> Model: poisson_glm_lm
#>
#> 95% confidence intervals, adjusted loglikelihod with type = ''vertical''
#>
#> Symmetric:
#> lower upper
#> (Intercept) 0.89907 1.22747
#> x 0.78985 1.20229
#> I(x^2) -0.12024 0.02199
#>
#> Profile likelihood-based:
#> lower upper
#> (Intercept) 0.8954 1.2232
#> x 0.7877 1.1991
#> I(x^2) -0.1198 0.0222
# Generate a nested model from fm_pois_adj
fm_pois_small_adj <- update(fm_pois_adj, . ~ . - I(x^2))
lmtest::coeftest(fm_pois_small_adj)
#>
#> z test of coefficients:
#>
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 1.05525 0.08111 13.010 < 2.2e-16 ***
#> x 0.90172 0.06939 12.995 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Perform an adjusted likelihood ratio test on the two models
anova(fm_pois_adj, fm_pois_small_adj)
#> Analysis of Adjusted Deviance Table
#>
#> Model 1: y ~ x + I(x^2)
#> Model 2: y ~ x
#>
#> Resid.df df ALRTS Pr(>ALRTS)
#> 1 247
#> 2 248 1 1.8202 0.1773
# Similarly, specify to remove I(x^2) from the larger model
alrtest(fm_pois_adj, "I(x^2)")
#> Adjusted likelihood ratio test
#>
#> Model 1: y ~ x + I(x^2)
#> Model 2: y ~ x
#>
#> Resid.df df ALRTS Pr(>ALRTS)
#> 1 247
#> 2 248 1 1.8202 0.1773
# Plot confidence regions for the parameter estimates
fm_pois_adj_vert <-
chandwich::conf_region(fm_pois_adj, which_pars = c("x", "I(x^2)"))
#> Waiting for profiling to be done...
fm_pois_adj_none <-
chandwich::conf_region(fm_pois_adj,
which_pars = c("x", "I(x^2)"),
type = "none"
)
#> Waiting for profiling to be done...
plot(
fm_pois_adj_vert,
fm_pois_adj_none,
conf = c(60, 80, 90, 95),
col = c("brown", "darkgreen"),
lty = c(1, 2),
lwd = 2.5
)
More information on the different methods can be found in the Introducing chantrics vignette, and in the corresponding help pages.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.