Analysis of Covariance With Qualitative Data
NBER Working Paper No. 325 (Also Reprint No. r0286)
In data with a group structure, incidental parameters are included to control for missing variables. Applications include longitudinal data and sibling data. In general, the joint maximum likelihood estimator of the structural parameters is not consistent as the number of groups increases, with a fixed number of observations per group. Instead a conditional likelihood function is maximized, conditional on sufficient statistics for the incidental parameters. In the logit case, a standard conditional logit program can be used. Another solution is a random effects model, in which the distribution of the incidental parameters may depend upon the exogenous variables.
Published: Chamberlain, Gary. "Analysis of Covariance With Qualitative Data." Review of Economic Studies, Vol. XLVII(1), No. 146 (January, 1980), pp. 225-238.