Odels with panel or other clustered data (Chamberlain 1980; Maddala 1983). Equivalently, discrete choice L868275 site models with unmeasured heterogeneity and repeated measures can be regarded as a species of multilevel model, in which the levels include individuals, alternatives in the choice sets of individuals, and time-specific alternatives. Issues of identification and estimation of these models for residential choice parallel those for the general multilevel model. (See Skrondal and RabeHesketh 2004 for a more detailed discussion of discrete choice models with unmeasured heterogeneity and their relationship to other multilevel models). Functional Form Discrete choice models allow the analyst to specify a variety of ways that people may respond to characteristics of neighborhoods. For example, in models of the relationship between neighborhood racial composition and the probability of entering or leaving a neighborhood, it is not just the average level of tolerance that matters but also the shape of the response curve. Schelling (1971; 1978) showed that a very high level of segregation results when individuals have a threshold response to the proportion own-group in their neighborhood ?that is, when people are indifferent to neighborhood characteristics within some interval and only care about whether a neighborhood characteristic is above or below the threshold. In a simple model where only neighborhood characteristic Zj enters into the choice equation, the utility in a threshold specification is(3.10)NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscriptwhere the threshold is a specific value of Zj. An alternative behavioral response is that people have a continuous response to neighborhood composition; in other words they are sensitive to even small changes in composition regardless of the actual level of the compositional variable. That is, utility is a continuous specification of neighborhood composition, e.g. Uij = Zj. Additionally, a number of intermediate functional form specifications allow for indifference over some intervals of neighborhood composition with a threshold response at key points. These functional form assumptions about how people respond to neighborhoods have implications for neighborhood turnover and segregation I-CBP112 supplier dynamics. Bruch and Mare (2006, 2009) show how the shape of choice functions affects segregation dynamics. Models for Ranked Data The discrete choice models discussed thus far assume that the analyst observes only the chosen alternative and has no information on the relative utilities of unchosen alternatives. Stated preference data, however, may provide information on full or partial ranking of alternatives, albeit for a hypothetical choice set (Allison and Christakis 1994).10 Ties occur10Ranked preference data arise from situations in which individuals are asked to pick their most preferred option among all available (for example, among a set of neighborhood vignettes), their (next) most preferred option among those that remain, and so on until all options have been ranked. This is a generalization of the standard discrete choice problem. Allison and Christakis (1994) provide further details about this choice model.Sociol Methodol. Author manuscript; available in PMC 2013 March 08.Bruch and MarePagein the data when respondents assign multiple items the same rank, and incomplete rankings occur when respondents leave certain items unranked. In this case, we observe groups of items that are ra.Odels with panel or other clustered data (Chamberlain 1980; Maddala 1983). Equivalently, discrete choice models with unmeasured heterogeneity and repeated measures can be regarded as a species of multilevel model, in which the levels include individuals, alternatives in the choice sets of individuals, and time-specific alternatives. Issues of identification and estimation of these models for residential choice parallel those for the general multilevel model. (See Skrondal and RabeHesketh 2004 for a more detailed discussion of discrete choice models with unmeasured heterogeneity and their relationship to other multilevel models). Functional Form Discrete choice models allow the analyst to specify a variety of ways that people may respond to characteristics of neighborhoods. For example, in models of the relationship between neighborhood racial composition and the probability of entering or leaving a neighborhood, it is not just the average level of tolerance that matters but also the shape of the response curve. Schelling (1971; 1978) showed that a very high level of segregation results when individuals have a threshold response to the proportion own-group in their neighborhood ?that is, when people are indifferent to neighborhood characteristics within some interval and only care about whether a neighborhood characteristic is above or below the threshold. In a simple model where only neighborhood characteristic Zj enters into the choice equation, the utility in a threshold specification is(3.10)NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscriptwhere the threshold is a specific value of Zj. An alternative behavioral response is that people have a continuous response to neighborhood composition; in other words they are sensitive to even small changes in composition regardless of the actual level of the compositional variable. That is, utility is a continuous specification of neighborhood composition, e.g. Uij = Zj. Additionally, a number of intermediate functional form specifications allow for indifference over some intervals of neighborhood composition with a threshold response at key points. These functional form assumptions about how people respond to neighborhoods have implications for neighborhood turnover and segregation dynamics. Bruch and Mare (2006, 2009) show how the shape of choice functions affects segregation dynamics. Models for Ranked Data The discrete choice models discussed thus far assume that the analyst observes only the chosen alternative and has no information on the relative utilities of unchosen alternatives. Stated preference data, however, may provide information on full or partial ranking of alternatives, albeit for a hypothetical choice set (Allison and Christakis 1994).10 Ties occur10Ranked preference data arise from situations in which individuals are asked to pick their most preferred option among all available (for example, among a set of neighborhood vignettes), their (next) most preferred option among those that remain, and so on until all options have been ranked. This is a generalization of the standard discrete choice problem. Allison and Christakis (1994) provide further details about this choice model.Sociol Methodol. Author manuscript; available in PMC 2013 March 08.Bruch and MarePagein the data when respondents assign multiple items the same rank, and incomplete rankings occur when respondents leave certain items unranked. In this case, we observe groups of items that are ra.
