Suppose dependent variable has more than two possible discrete outcomes. I wonder what is the difference between fitting a multinomial logistic regression model and several pairwise binary logistic regression models?
Do they return the p-values of coefficients?
# ------- Edit.
I did a comparison between multinational logistic regression and binomial logistic regression in R. They gave a different result. Hope someone could help.
Suppose I am interested in what is the odds ratio of being in pier and beach given one-unit of income increase. Fishing$mode has four classes, beach, pier, boat and charter.
In the multinomial scenario, I used following code to get the p value.
library("nnet")
data("Fishing", package = "mlogit")
fishing.mu <- multinom(mode ~ 1 + income, data = Fishing)
sum.fishing <- summary(fishing.mu) # gives a table of outcomes by covariates for coef and SE
# now get the p values by first getting the t values
pt(abs(sum.fishing$coefficients / sum.fishing$standard.errors),
df=nrow(Fishing)-6,lower=FALSE)*2
# (Intercept) income
# pier 0 9.271562e-08
# boat 0 8.725280e-06
# charter 0 1.352088e-01
the p value of the coefficient of income is 9.271562e-08. Then I fit a logistic regression using a subset of data, mode%in%c("beach","pier").
mylogit <- glm(mode ~ income, data = Fishing, family = binomial(link = "logit"),
subset=mode%in%c("beach","pier"))
summary(mylogit)
# Call:
# glm(formula = mode ~ income, family = binomial(link = "logit"),
# data = Fishing, subset = mode %in% c("beach", "pier"))
#
# Deviance Residuals:
# Min 1Q Median 3Q Max
# -1.4658 -1.2976 0.9499 1.0238 1.4920
#
# Coefficients:
# Estimate Std. Error z value Pr(>|z|)
# (Intercept) 7.037e-01 2.126e-01 3.310 0.000932 ***
# income -1.135e-04 4.817e-05 -2.356 0.018495 *
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# (Dispersion parameter for binomial family taken to be 1)
#
# Null deviance: 426.30 on 311 degrees of freedom
# Residual deviance: 420.58 on 310 degrees of freedom
# AIC: 424.58
#
# Number of Fisher Scoring iterations: 4
this time, the p value of the coefficient of income becomes 0.018495.
Why does this happen? Did I miss anything?
