Robustness of linear models in dynamic multivariate predictions

Linear aggregation models employing unit and equal weights have been shown to be superior to human decisions in a surprising range of decision situations. In addition, decisions based on these models have often been found to be superior to those based on linear regression models (LRMs). This general issue was explored for repetitive decisions in production planning. The problem considered differs in several aspects from the types of problems investigated previously: (1) the problem is dynamic rather than static; (2) a set (or vector) of interactive decisions dependent on previous decisions is required to be made, where a decision in stage t, the dependent variable, becomes an independent variable in stage t + 1; and (3) the criterion function is cost with a quadratic loss function (rather than the correlation measure of R2). Moreover, since repetitive decisions were involved, the parameters of the models were estimated using past human decisions. These were used to predict specific values of the decision variables (rather than rank order), which in turn were employed recursively to predict values of the decision variables at subsequent stages. While decisions from equal weighting rules were found to be superior to human decisions and not greatly inferior to decisions from linear regression models, decisions from unit weighting rules performed poorly. The rationale for such performance is discussed, indicating that previous theoretical and empirical research on linear weighting models is not generally applicable to dynamic, multivariate interactive decisions problems with lagged variables.