The positivity constraint (not enforced on the intercepts) described in equation (8) is the methodological nuance in this manuscript that is added to the DeSarbo and Cron (1988) procedure given the a priori theoretical structure implied between specified firm capabilities ð _X Þ and profitability ð _y Þ in the application. Given the RBV theory which postulates positive effects for capabilities (it is indeed intuitive to believe that more of a capability or resource cannot possibly decrease performance), problems of multi-collinearity can often flip signs in such linear models. This is even more of a potential problem in clusterwise regression in which the sample size is sequentially partitioned into groups (DeSarbo and Edwards, 1996). Unfortunately, the addition of such constraints complicates the computational aspect of the proposed new methodology as shown in Appendix 1.
Thus, we use basically the same information/data as in traditional regression analysis, but now are able to simultaneously estimate discrete groups or clusters of firms, their sizes and membership, as well as the group level regression coefficients.
Note that once estimates of l k ; s2
k ; and b jk are obtained within any iterate, one can
assign each firm i to each cluster or group k (conditioned on these estimates) using
Bayes’ rule via the estimated posterior probability:
The positivity constraint (not enforced on the intercepts) described in equation (8) is the methodological nuance in this manuscript that is added to the DeSarbo and Cron (1988) procedure given the a priori theoretical structure implied between specified firm capabilities ð _X Þ and profitability ð _y Þ in the application. Given the RBV theory which postulates positive effects for capabilities (it is indeed intuitive to believe that more of a capability or resource cannot possibly decrease performance), problems of multi-collinearity can often flip signs in such linear models. This is even more of a potential problem in clusterwise regression in which the sample size is sequentially partitioned into groups (DeSarbo and Edwards, 1996). Unfortunately, the addition of such constraints complicates the computational aspect of the proposed new methodology as shown in Appendix 1.Thus, we use basically the same information/data as in traditional regression analysis, but now are able to simultaneously estimate discrete groups or clusters of firms, their sizes and membership, as well as the group level regression coefficients.Note that once estimates of l k ; s2k ; and b jk are obtained within any iterate, one canassign each firm i to each cluster or group k (conditioned on these estimates) usingBayes’ rule via the estimated posterior probability:
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