问题
I am using the 'bife' package to run the fixed effect logit model in R. However, I cannot compute any goodness-of-fit to measure the model's overall fit given the result I have below. I would appreciate if I can know how to measure the goodness-of-fit given this limited information. I prefer chi-square test but still cannot find a way to implement this either.
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Fixed effects logit model
with analytical bias-correction
Estimated model:
Y ~ X1 +X2 + X3 + X4 + X5 | Z
Log-Likelihood= -9153.165
n= 20383, number of events= 5104
Demeaning converged after 6 iteration(s)
Offset converged after 3 iteration(s)
Corrected structural parameter(s):
Estimate Std. error t-value Pr(> t)
X1 -8.67E-02 2.80E-03 -31.001 < 2e-16 ***
X2 1.79E+00 8.49E-02 21.084 < 2e-16 ***
X3 -1.14E-01 1.91E-02 -5.982 2.24E-09 ***
X4 -2.41E-04 2.37E-05 -10.171 < 2e-16 ***
X5 1.24E-01 3.33E-03 37.37 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
AIC= 18730.33 , BIC= 20409.89
Average individual fixed effects= 1.6716
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回答1:
Let the DGP be
n <- 1000
x <- rnorm(n)
id <- rep(1:2, each = n / 2)
y <- 1 * (rnorm(n) > 0)
so that we will be under the null hypothesis. As it says in ?bife
, when there is no bias-correction, everything is the same as with glm
, except for the speed. So let's start with glm
.
modGLM <- glm(y ~ 1 + x + factor(id), family = binomial())
modGLM0 <- glm(y ~ 1, family = binomial())
One way to perform the LR test is with
library(lmtest)
lrtest(modGLM0, modGLM)
# Likelihood ratio test
#
# Model 1: y ~ 1
# Model 2: y ~ 1 + x + factor(id)
# #Df LogLik Df Chisq Pr(>Chisq)
# 1 1 -692.70
# 2 3 -692.29 2 0.8063 0.6682
But we may also do it manually,
1 - pchisq(c((-2 * logLik(modGLM0)) - (-2 * logLik(modGLM))),
modGLM0$df.residual - modGLM$df.residual)
# [1] 0.6682207
Now let's proceed with bife
.
library(bife)
modBife <- bife(y ~ x | id)
modBife0 <- bife(y ~ 1 | id)
Here modBife
is the full specification and modBife0
is only with fixed effects. For convenience, let
logLik.bife <- function(object, ...) object$logl_info$loglik
for loglikelihood extraction. Then we may compare modBife0
with modBife
as in
1 - pchisq((-2 * logLik(modBife0)) - (-2 * logLik(modBife)), length(modBife$par$beta))
# [1] 1
while modGLM0
and modBife
can be compared by running
1 - pchisq(c((-2 * logLik(modGLM0)) - (-2 * logLik(modBife))),
length(modBife$par$beta) + length(unique(id)) - 1)
# [1] 0.6682207
which gives the same result as before, even though with bife
we, by default, have bias correction.
Lastly, as a bonus, we may simulate data and see it the test works as it's supposed to. 1000 iterations below show that both test (since two tests are the same) indeed reject as often as they are supposed to under the null.
来源:https://stackoverflow.com/questions/53206564/goodness-of-fit-for-fixed-effect-logit-model-using-bife-package