------------------------------------------------------------------------------- help forcrtestJoao Pedro W. de Azevedo -------------------------------------------------------------------------------

Cramer-Ridder Test for pooling states in aMultinomial Logit

crtest

Description

crtestperforms the Cramer-Ridder test for pooling states in the Multinomial logit model.

Examples

.mlogit occup1 female under35 married2.crtest

Technical detailsThis test assume a multinomial logit model with (S+1) states and two states that are candidates for pooling, s1 and s2. The null hypothesis is that s1 and s2 have the same regressors coefficient apart from the intercept, or

Bs1 = Bs2 = Bs (1) To test this hypothesis the following test statistics can be used: LR = 2{lnL - lnLr} (2) where lnL is the maximum log likelihood of the original model and lnLr the maximum log likelihood if the estimates are constrained to satisfy (1). LR asymptotically has a chi-square distribution with k degrees of freedom where k is the number of restrictions implied by (1). LnL is readily available from the original model, but the lnLr apparently requires constrained estimation which can be quite laborious.

Cramer and Ridder (1991) show that the lnLr can be easily derived from an unconstrained estimation of the pooled model with only S states. The following expression to estimate the restricted maximum log likelihood is then presented by the authors,

lnLr = ns1*ln(ns1) + ns2*ln(ns2) - ns*ln(ns) + lnLp

where lnLp is the unconstrained maximum of the log likelihood of the pooled model. ns1 and ns2 are the number of observations on the states s1 and s2, respectively, and ns = ns1 + ns2.

References

Cramer,J.S. and G.Ridder (1991) "Pooling states in multinomial logit model."

Journal of Econometrics, 47: 267-272.

AuthorsJoao Pedro W. de Azevedo, University of Newcastle, UK j.p.azevedo@ncl.ac.uk

AknowledgementsThis ado file uses the auxiliary ado file _pecats written by J. Scott Long and Jeremy Freese. I would like to thank Brian Poi, Christopher Baum and Nick Cox for their helpfull suggestions. As usual, all mistakes are of my own responsibility.

Also seeManual:

[R] mlogitOnline: help for mlogtest; iia; smhsiao (if installed)