And the number of alternatives. Thus if one has sufficient observations

Thus if one has sufficient observations, it is more fruitful to analyze a sample of many observations with a small number of sampled alternatives GLPG0187 site rather than fewer observations with a large number of alternatives (Ben-Akiva and Lerman 1985:263). Whereas this stratification scheme jir.2014.0149 may be exogenous for some analytic purposes, it results in endogenous stratification for the study of neighborhood choice. Neighborhood stratified samples, therefore, are choice-based (Manski and Lerman 1977), in that the sampling procedure is confounded with the residential choices of the respondents. Without correction for sample design, estimates of parameters in discrete choice models are not, fpsyg.2015.00360 in general, consistent. If choice-based sampling probabilities are known, however, one can obtain consistent estimates of the model parameters using sampling weights. Manski and Lerman (1977) introduce an estimator in which each observed residential choice is weighted by its representation in the population as a whole. We define a function for each respondent,(4.5)SCR7 chemical information NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscriptwhere Vi denotes the population shares and Hi denotes the sample shares for that respondent's type. These weights enter the likelihood function for the model as:(4.6)In practice, the correction weights for choice-based sampling can be estimated using the "importance weights" option in statistical estimation packages. For example, consider a sample of households where the proportion of respondents in high poverty neighborhoods (30 of households below the poverty line) and low poverty neighborhoods (