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

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Neighborhood stratified samples, therefore, are choice-based (Manski and Lerman 1977), in that the sampling Title Loaded From File procedure is confounded with the residential choices of the respondents. For example, surveys may oversample poor neighborhoods within a city or be drawn from schools or school districts with atypical minority or socioeconomic representation.And the number of alternatives. Thus if one has sufficient observations, it is more fruitful to analyze a sample of many observations with a small number of sampled alternatives rather than fewer observations with a large number of alternatives (Ben-Akiva and Lerman 1985:263). In practice, one can do sensitivity analyses to determine how alternative subsampling probabilities affect the estimated coefficients and standard errors. For example, one can vary the subsampling fraction and pick the smallest fraction that does not result in marked loss of precision of estimates. Choice Based Sampling Many surveys employ a form of stratified sampling that overrepresents some kinds of neighborhoods and underrepresents others. For example, surveys may oversample poor neighborhoods within a city or be drawn from schools or school districts with atypical minority or socioeconomic representation. 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)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 (