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testing hypotheses about path models, model trimming, depends in part in how a model is derived, aic=x^2-2df, guided by researchers hypotheses, lower aic is preffered, differnce between the x^2 values of 2 hiearchical models, nonsignificant, theorectical (not mathematical) grounds, model trimming only, nonsignificant decrement in overall fit when a parameter is eliminated, model building, respecificatinon that capitalizes on chance variation, start w overidentified model to which paths are added, theoretical, testing hypotheses about path models, parsimoneous model that fits the data well, akaike information criterion (aic), empirical, degrees of freedom = difference between the two values, why should one model be preffered over mathematically equivalent models, x^2 increases (fit decreases), competing theories, consider equivalent models (stelzl, 1986), comparison of hierarchical models (nested models), comparable fit, dropped from the model, two path models are hierarchical if one is a subset of the other, significant, chi-square difference (x^2difference) test, constraint (parameter =0) for 1 parameters, suggests model has been simplified too much, estimates the amout of model's ovearll x^2 would increase if a particular free parameter were fixed to zero (i.e., dropped from the model), lee-hershberger replacing rules (hershberger, 1994 lee & hershberger, 1990), similar to type ii error, wald (w) statistic, supports retention of the path(s) that was just added, added to the model, empirical, nonsignificant, yield the same predicted correlations or covariances, but they do so w a different configuration of paths among the same variables, x^2 statistics from two nonhierarchical models, releasing of a constraint (parameter previously = 0 is released), theoretical, start w just identified model and eliminate paths, compare nonhieararchical models, similar to type i error, x^2 decreases (fit improves), if a deleted path is also predicted in advance to be zero, then the x^2 difference test is of utmost theoretical interest, based on statistical criteria, includes a penalty for rcomplexity