[R] Likelihood ratio test for proportional odds logistic regression
xinyi lin
x1lin at ucsd.edu
Sat Jan 5 14:14:23 CET 2008
Hi,
I want to do a global likelihood ratio test for the proportional odds
logistic regression model and am unsure how to go about it. I am using
the polr() function in library(MASS).
1. Is the p-value from the likelihood ratio test obtained by
anova(fit1,fit2), where fit1 is the polr model with only the intercept
and fit2 is the full polr model (refer to example below)? So in the
case of the example below, the p-value would be 1.
2. For the model in which there is only one independent variable, I
would expect the Wald test and the likelihood ratio test to give
similar p-values. However the p-values obtained from anova(fit1,fit3)
(refer to example below) are very different (0.0002622986 vs. 1). Why
is this so?
> library(MASS)
> fit1 <- polr(housing$Sat~1)
> fit2<- polr(housing$Sat~housing$Infl)
> fit3<- polr(housing$Sat~housing$Cont)
> summary(fit1)
Re-fitting to get Hessian
Call:
polr(formula = housing$Sat ~ 1)
No coefficients
Intercepts:
Value Std. Error t value
Low|Medium -0.6931 0.2500 -2.7726
Medium|High 0.6931 0.2500 2.7726
Residual Deviance: 158.2002
AIC: 162.2002
> summary(fit2)
Re-fitting to get Hessian
Call:
polr(formula = housing$Sat ~ housing$Infl)
Coefficients:
Value Std. Error t value
housing$InflMedium 6.347464e-06 0.5303301 1.196889e-05
housing$InflHigh 6.347464e-06 0.5303301 1.196889e-05
Intercepts:
Value Std. Error t value
Low|Medium -0.6931 0.3953 -1.7535
Medium|High 0.6932 0.3953 1.7536
Residual Deviance: 158.2002
AIC: 166.2002
> summary(fit3)
Re-fitting to get Hessian
Call:
polr(formula = housing$Sat ~ housing$Cont)
Coefficients:
Value Std. Error t value
housing$ContHigh 0.0001135777 0.4330091 0.0002622986
Intercepts:
Value Std. Error t value
Low|Medium -0.6931 0.3307 -2.0956
Medium|High 0.6932 0.3307 2.0960
Residual Deviance: 158.2002
AIC: 164.2002
> anova(fit1,fit2)
Likelihood ratio tests of ordinal regression models
Response: housing$Sat
Model Resid. df Resid. Dev Test Df LR stat. Pr(Chi)
1 1 70 158.2002
2 housing$Infl 68 158.2002 1 vs 2 2 -6.375558e-10 1
> anova(fit1,fit3)
Likelihood ratio tests of ordinal regression models
Response: housing$Sat
Model Resid. df Resid. Dev Test Df LR stat. Pr(Chi)
1 1 70 158.2002
2 housing$Cont 69 158.2002 1 vs 2 1 -1.224427e-07 1
Thank you,
Xinyi
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