Estimate the parameters of the discrete choice model. If the ij follow a type I extreme value (Gumbel) distribution, we obtain a conditional logit model,(3.4)where C(i) denotes the choice set for the ith individual, which may be restricted to incorporate discrimination, prices, or information constraints (McFadden 1978). For example, the choice set may be restricted to units within a given radius of a person’s current home, to units in neighborhoods that are at least 10 percent own-race, or to units where monthly rent or mortgage payments would be less than some fraction of individuals’ incomes. Typically these models are estimated using maximum likelihood, where the likelihood is:(3.5)Early applications of the basic discrete choice model to residential mobility analysis include McFadden (1978) and Lerman (1975). Gabriel and Rosenthal (1989) use a multinomial logit4Most standard statistical software packages can be used to estimate the basic discrete choice models discussed in this section (that is, those that do not include unmeasured heterogeneity), either as a conditional logit, fixed effects logit, or multinomial logit model.Sociol Methodol. Author manuscript; available in PMC 2013 March 08.Bruch and MarePagemodel to examine how race and other traits of individuals affect residential mobility among five counties in the Washington DC area. Sermons and Koppelman (2001) estimate a discrete choice model of residential choice that explores how men and women differ in their sensitivity to commuting time.5 Independence from Irrelevant Alternatives Assumption The conditional logit form of the discrete choice model assumes independence from irrelevant alternatives, (IIA). It is a model for pairwise comparison and assumes that the odds of preferring an alternative in a pairwise comparison is unCPI-455 manufacturer affected by the other available alternatives. That is, after accounting for observable features of choices, the remaining (unobserved) features of choices are uncorrelated (that is, E [ij,ik] = 0). IIA is really an assumption about proper model specification which implies that there is no omitted variable bias and also that the choice set is exhaustive and well defined (McFadden, Train, and Tye 1981). The IIA property implies that the ratio of probabilities for any two choices is unaffected by the utilities of all other alternatives implying that the ratio is not affected by the addition or exclusion of alternatives. The conditional probability of choosing the jth neighborhood given a choice between neighborhood j or k is(4.3)Mirogabalin manufacturer NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author ManuscriptThis probability does not depend on the traits of neighborhoods other than j and k. If valid, this assumption makes it possible to estimate choice models on a subset of alternatives in the choice set. Additionally, one can make out-of-sample predictions because the parameter estimates from the model are invariant to the inclusion or exclusion of alternatives in individuals’ choice sets. However, in practice the IIA assumption is often not met. We rarely observe all attributes of destinations that affect mobility behavior. Some neighborhoods have similar characteristics and, were one of them omitted, individuals would disproportionately choose a similar neighborhood rather than distribute themselves proportionately across both similar and dissimilar neighborhoods. Unless the sources of similarity and dissimilarity among neighborhoods are controlled in the cho.Estimate the parameters of the discrete choice model. If the ij follow a type I extreme value (Gumbel) distribution, we obtain a conditional logit model,(3.4)where C(i) denotes the choice set for the ith individual, which may be restricted to incorporate discrimination, prices, or information constraints (McFadden 1978). For example, the choice set may be restricted to units within a given radius of a person’s current home, to units in neighborhoods that are at least 10 percent own-race, or to units where monthly rent or mortgage payments would be less than some fraction of individuals’ incomes. Typically these models are estimated using maximum likelihood, where the likelihood is:(3.5)Early applications of the basic discrete choice model to residential mobility analysis include McFadden (1978) and Lerman (1975). Gabriel and Rosenthal (1989) use a multinomial logit4Most standard statistical software packages can be used to estimate the basic discrete choice models discussed in this section (that is, those that do not include unmeasured heterogeneity), either as a conditional logit, fixed effects logit, or multinomial logit model.Sociol Methodol. Author manuscript; available in PMC 2013 March 08.Bruch and MarePagemodel to examine how race and other traits of individuals affect residential mobility among five counties in the Washington DC area. Sermons and Koppelman (2001) estimate a discrete choice model of residential choice that explores how men and women differ in their sensitivity to commuting time.5 Independence from Irrelevant Alternatives Assumption The conditional logit form of the discrete choice model assumes independence from irrelevant alternatives, (IIA). It is a model for pairwise comparison and assumes that the odds of preferring an alternative in a pairwise comparison is unaffected by the other available alternatives. That is, after accounting for observable features of choices, the remaining (unobserved) features of choices are uncorrelated (that is, E [ij,ik] = 0). IIA is really an assumption about proper model specification which implies that there is no omitted variable bias and also that the choice set is exhaustive and well defined (McFadden, Train, and Tye 1981). The IIA property implies that the ratio of probabilities for any two choices is unaffected by the utilities of all other alternatives implying that the ratio is not affected by the addition or exclusion of alternatives. The conditional probability of choosing the jth neighborhood given a choice between neighborhood j or k is(4.3)NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author ManuscriptThis probability does not depend on the traits of neighborhoods other than j and k. If valid, this assumption makes it possible to estimate choice models on a subset of alternatives in the choice set. Additionally, one can make out-of-sample predictions because the parameter estimates from the model are invariant to the inclusion or exclusion of alternatives in individuals’ choice sets. However, in practice the IIA assumption is often not met. We rarely observe all attributes of destinations that affect mobility behavior. Some neighborhoods have similar characteristics and, were one of them omitted, individuals would disproportionately choose a similar neighborhood rather than distribute themselves proportionately across both similar and dissimilar neighborhoods. Unless the sources of similarity and dissimilarity among neighborhoods are controlled in the cho.
