E to estimate model that allows for correlation in the attractiveness of observations within or among individuals. Several models are available to represent correlation of attractiveness across observations, including the nested and mixed logit models. We discuss these in turn. Nested Logit Models–Nested logit models may solve the problem of unmeasured neighborhood heterogeneity if unmeasured characteristics of alternatives can be accounted for by conditioning on the appropriate choice subset. For example, if the choice set is all CPI-455MedChemExpress CPI-455 neighborhoods within the Detroit Metropolitan Area, but all the neighborhoods within the Grosse 4-Deoxyuridine site Pointe area of Detroit share key attributes (zoning regulation, funding for schools, etc.), at least some of which are unmeasured, we can treat Grosse Pointe neighborhoods as a subset. Subsets or “nests” are alternatives that are similar along one or more dimensions not accounted for in the formal discrete choice model. The nested logit model partitions the choice set C into N “nests,” Cn such that the complete choice set . Nests can represent a decision sequence (e.g., people first choose a region of the country, then a city, and then a neighborhood) or account for attributes of alternatives that make them more similar in both their observed and unobserved characteristics. The nests are constructed such that, for any two alternatives that are within the same nest, the ratio of probabilities is independent of the existence of all other alternatives.7 The nesting structure assumes that: (1) neighborhoods that are in the same nests share unobserved features and (2) neighborhoods across nests do not share these unobserved features. That is, choices may have correlated unobservables within nests but not between them.8 Whereas in the simple conditional logit model, disturbances are independent and follow a univariate extreme value distribution, in the nested logit, the marginal distribution7Nested logit models can be estimated in most standard statistical software packages, including Stata, SAS, R and the Limdep package NLOGIT. 8The standard nested logit, assumes a simple hierarchical classification of alternatives within nests. Wen and Koppelman (2001) define a generalized nested logit that allows for more flexible substitution patterns.Sociol Methodol. Author manuscript; available in PMC 2013 March 08.Bruch and MarePageof the disturbances across nests follows a univariate extreme value distribution, but the disturbances may be correlated within nests (Train 2003, Ch. 4). To estimate the nested logit model, the nesting structure must be known to the analyst in advance, which is often not, the case.9 Resemblance of alternatives on unobserved traits for any subset of alternatives, moreover, is often not an all or nothing matter but rather a matter of degree. These considerations give rise to the need for a more flexible model for unobserved heterogeneity. Mixed Logit Model–Mixed logit models are a more general class of models that can accommodate both alternative- and individual-specific unmeasured heterogeneity, and are useful if the analyst believes that the unobserved heterogeneity is correlated with observable characteristics of neighborhoods. The model is an extension of (3.4). In particular, the error component ij is broken out into two parts; that is,(3.6)NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscriptwhere i is an individual-specific (alternative invariant) random vector with zero mean.E to estimate model that allows for correlation in the attractiveness of observations within or among individuals. Several models are available to represent correlation of attractiveness across observations, including the nested and mixed logit models. We discuss these in turn. Nested Logit Models–Nested logit models may solve the problem of unmeasured neighborhood heterogeneity if unmeasured characteristics of alternatives can be accounted for by conditioning on the appropriate choice subset. For example, if the choice set is all neighborhoods within the Detroit Metropolitan Area, but all the neighborhoods within the Grosse Pointe area of Detroit share key attributes (zoning regulation, funding for schools, etc.), at least some of which are unmeasured, we can treat Grosse Pointe neighborhoods as a subset. Subsets or “nests” are alternatives that are similar along one or more dimensions not accounted for in the formal discrete choice model. The nested logit model partitions the choice set C into N “nests,” Cn such that the complete choice set . Nests can represent a decision sequence (e.g., people first choose a region of the country, then a city, and then a neighborhood) or account for attributes of alternatives that make them more similar in both their observed and unobserved characteristics. The nests are constructed such that, for any two alternatives that are within the same nest, the ratio of probabilities is independent of the existence of all other alternatives.7 The nesting structure assumes that: (1) neighborhoods that are in the same nests share unobserved features and (2) neighborhoods across nests do not share these unobserved features. That is, choices may have correlated unobservables within nests but not between them.8 Whereas in the simple conditional logit model, disturbances are independent and follow a univariate extreme value distribution, in the nested logit, the marginal distribution7Nested logit models can be estimated in most standard statistical software packages, including Stata, SAS, R and the Limdep package NLOGIT. 8The standard nested logit, assumes a simple hierarchical classification of alternatives within nests. Wen and Koppelman (2001) define a generalized nested logit that allows for more flexible substitution patterns.Sociol Methodol. Author manuscript; available in PMC 2013 March 08.Bruch and MarePageof the disturbances across nests follows a univariate extreme value distribution, but the disturbances may be correlated within nests (Train 2003, Ch. 4). To estimate the nested logit model, the nesting structure must be known to the analyst in advance, which is often not, the case.9 Resemblance of alternatives on unobserved traits for any subset of alternatives, moreover, is often not an all or nothing matter but rather a matter of degree. These considerations give rise to the need for a more flexible model for unobserved heterogeneity. Mixed Logit Model–Mixed logit models are a more general class of models that can accommodate both alternative- and individual-specific unmeasured heterogeneity, and are useful if the analyst believes that the unobserved heterogeneity is correlated with observable characteristics of neighborhoods. The model is an extension of (3.4). In particular, the error component ij is broken out into two parts; that is,(3.6)NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscriptwhere i is an individual-specific (alternative invariant) random vector with zero mean.