I am using the package nnet to fit multinomial regression models using multinom().
When fitting the model using an independent variable with much greater mean than variance, the confidence intervals get narrower and the p-value gets smaller. This is unexpected behavior for me.
As a simple univariate example I modified the given example on the multinom() help page. I will ilustrate it using the confint.multinom() function from the same package, since p-values are not natively supported by nnet.
library(MASS)
example(birthwt)
######## Base Line glm logistic Regression #############
glm_model <- glm(formula = low ~ age, family = binomial, data = bwt)
confint(glm_model)
2.5 % 97.5 %
(Intercept) -1.0336270 1.847399861
age -0.1150799 0.008986436
######## Base Line multinomial logistic Regeression ###########
multinom_model <- multinom(formula = low ~ age, data = bwt)
confint(multinom_model)
# weights: 3 (2 variable)
initial value 131.004817
final value 115.955980
converged
2.5 % 97.5 %
(Intercept) -1.0494438 1.8205227
age -0.1129621 0.0105759
######## Transformed glm logistic Regression ###########
glm_model_mod <- glm(formula = low ~ I(age+200), family = binomial, data = bwt)
confint(glm_model_mod)
2.5 % 97.5 %
(Intercept) -2.8001518 24.832982980
I(age + 200) -0.1150799 0.008986436
######## Transformed multinomial logistic Regeression ###########
multinom_model_mod <- multinom(low ~ I(age+200), data=bwt)
confint(multinom_model_mod)
# weights: 3 (2 variable)
initial value 131.004817
iter 10 value 115.984705
final value 115.955988
converged
2.5 % 97.5 %
(Intercept) 10.64489882 10.64491130
I(age + 200) -0.05267766 -0.04989515
At first the confidence intervals of multinom are a bit more conservative compared to glm. But when adding 200 to the independent variable, the confidence intervals are getting extremely narrow and even the coefficient for age changes (-0.05119 -> -0.05128). The coefficient for age of the normal logistic regression is, as expected, unaffected by this intercept change.
This example also holds for real multinomial models with a 3 level dependent variable and models with multiple independent variables.
Am I violating model assumptions? Or am I misunderstanding how the multinomial regression works?
