| This study examined the performance of two computation-intensive methods for estimating the standard errors of estimators for a form of causal equation analysis known as Factorial Modeling (FaM) (Lohnes, 1979). FaM is a causal modeling method which sequentially extracts user-defined orthogonal factors. Because the sampling distribution of FaM coefficients is not in general known, tests of the statistical significance of most FaM coefficients are not presently available.; Two methods of estimating standard errors for unknown sampling distributions were evaluated. The first of these, the jackknife method (Tukey, 1958), obtains an estimate of the standard error by examining the contribution of each case to a point estimator. The other method, the bootstrap (Efron, 1979), is a collection of methods in which a large number of subsamples of the same size as the original sample are taken with replacement. The sampling error of the statistic of interest is found by repeatedly computing the statistic for each subsample and using the resulting ordered set of statistics as an approximation of the sampling distribution.; The methods were examined by observing their performance across 500 Monte Carlo samples from a four variable population with multi-normal distribution. The FaM model examined had two factors (the first one a single-indicator factor and the second one a two-indicator factor) and a single criterion. Three bootstrap standard error estimators were obtained by varying the number of bootstrap samples taken (n = 250, 500, and 1,000). Jackknife and bootstrap estimates were compared against empirically-generated standard errors based on 4,000 Monte Carlo samples.; Results suggested that although bootstrapping in general produced the least-biased estimates of standard errors, in general jackknifing produced the best estimates when bias and efficiency were both taken into consideration. The standard error of multiple-indicator factor loadings were, however, poorly estimated with both methods. This problem occurs because FaM implicitly assumes that all input correlations may range between {dollar}-{dollar}1.0 and 1.0. These results suggest that jackknifing and bootstrapping must be used cautiously if they are to be employed by FaM. |
