A constrained laten t structure regression methodology
Let: k ¼ 1, .. . K derived cluster or group (unknown); i ¼ 1, .. . I firms; j ¼ 1, .. . J
independent variables (here, capabilities); yi ¼ the value of the dependent variable for
firm i (here, profitability); Xij ¼ the value of the j th independent variable for firm i (i.e.
firm capabilities); bjk ¼ the value of the jth capability regression coefficient for cluster
or group k ; s2
k ¼ the variance term for the k th cluster or group; l k ¼ the mixing
proportion for the k th cluster or group.
DeSarbo and Cron (1988) modeled y i as a finite mixture of conditional univariate
normal densities: