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help for crtest                                        Joao Pedro W. de Azevedo
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Cramer-Ridder Test for pooling states in a Multinomial Logit


        crtest


Description


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

                
Examples


        .mlogit occup1 female under35 married2
        .crtest


Technical details

    This 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.

        
Authors

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


Aknowledgements

    This 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 see

    Manual:  [R] mlogit
    Online:  help for mlogtest; iia; smhsiao (if installed)