into an vector and the upper thresholds into another vector . Then, in matrix form, the measurement equation for the ordinal outcomes (indicators) for the decision-maker may be written as: . (5) For the count variable, let the index be g for the count categories and let r be the actual observed count value for the household. Then, a generalized version of the negative binomial count model may be written as (see Castro, Paleti, and Bhat, or CPB, 2012 and Bhat et al., 2013): (6) , , and . (7) In the above equation, is a latent continuous stochastic propensity variable that maps into the observed count r through the vector (which is a vertically stacked column vector of thresholds is an vector of latent variable loadings on the count outcome, and is a standard normal random error term. is a column vector corresponding to the vector (including a constant) of exogenous observable covariates and endogenous outcomes. in the threshold function of Equation (7) is the inverse function of the univariate cumulative standard normal. is a parameter that provides flexibility to the count formulation, and is related to the dispersion parameter in a traditional negative binomial model if the general negative binomial structure collapses to a general Poisson structure). is the traditional gamma function; . The threshold terms in the vector satisfy the ordering condition (i.e., as long as The presence of the terms in the thresholds provides substantial flexibility to accommodate high or low probability masses for specific count outcomes (see CPB, 2012 for a detailed discussion). For identification, set and . In addition, we identify a count value above which is held fixed at ; that is, if where the value of can be based on empirical testing. Doing so is the key to allowing the count model to predict beyond the count range available in the estimation sample. For later use, let ( vector) (assuming . Next, consider the nominal (unordered-response) outcome for the individual, and let i be the corresponding ( = 1, 2, 3,…, I). Let the individual under consideration choose the alternative . Also, assume the usual random utility structure for each alternative i. (8) where is the same fixed vector of exogenous variables as earlier, is an column vector of corresponding coefficients, and is a normal random error term. is a matrix of variables
2. Estimation Results of Structural Equation Variable Coefficient T-stat Green Lifestyle Propensity (GLP) Household income (base: 75,000 or more) Less than 25,000 0.702 12.001 25,000 – 34,999 0.523 7.234 35,000 – 49,999 0.401 6.944 50,000 – 74,999 0.198 7.104 Age (base: fraction of adults in the age group Fraction of adults in the age group -0.478 -9.623 Fraction of adults in the age group -0.331 -4.978 Fraction of adults in the age group 65 or more -0.132 -1.941 Gender (base: fraction of female adults in the household) Fraction of male adults in the household -0.029 -1.850 Education status (base: fraction of adults with less than a bachelor’s degree) Fraction of adults with a 0.160 4.101
bachelor’s degree Fraction of adults with an MS or PhD degree 0.203 2.103 Luxury Lifestyle Propensity (LLP) Household income (base: 75,000 or more) Less than 25,000 -0.201 -11.933 25,000 – 34,999 -0.322 -8.000 35,000 – 49,999 -0.431 -7.924 50,000 – 74,999 -0.472 -6.424 Number of children (less than 18 years old) in the household 0.473 11.926 Age (base: fraction of adults in the age Fraction of adults in the age group 0.130 3.553 Fraction of adults in the age group 0.412 3.567 Fraction of adults in the age group 65 or more 0.450 2.210 Correlation coefficient between ‘active attitude’ and ‘travel affinity/privacy -0.168 -5.421