A Comparison of Regression Prediction Accuracy on Several Types of Factor Scores

Abstract

Several advantages to the use of factor scores as independent variables in a multiple regression equation have been advocated in the literature To provide guidance for selecting the most desirable type of factor score upon which to calculate a regression equation, computer-based Monte Carlo methods were used to compare the predictive accuracy upon replication of regression on five "complete" and four "incomplete"factor score estimation methods. For several levels of multiple correlation (R 2 = .30, .50, and. 70), and for several subjectto-variable sampling ratios (3:1, 5:1, and 10:1), prediction on incomplete factor scores showed better double cross-validated prediction accuracy than on complete factor scores. Moreover, the unique unit-weighted factor score was superior among the incomplete methods.

The Predictive Accuracy of Full-Rank Variables Vs. Various Types of Factor Scores: Implications for Test Validation

“…The performance of each &dquo;purely&dquo; incomplete factor score type (excluding the Ideal/Loading type since it is a hybrid) was also contrasted with the aggregate of the non-incomplete factor score predictor types with results (Table 2) corroborating the superiority of incomplete factor scores as predictors as suggested previously (Morris, 1979). The results of that study are thus extended to a different data set.…”

“…However, the several types of factor scores in use appear to manifest differing degrees of replication prediction accuracy, with regression estimates performing least well (Morris, 1979).…”

“…Therefore, results may hopefully aid the researcher in maximizing the predictive capabilities of batteries of tests by suggesting the best kind of data (full-rank or a variety of reduced-rank scores) from which to predict. Method A procedure which was relatively parallel to that employed in a recent comparison of the replication predictive accuracies of five &dquo;complete&dquo; (some least-squares procedure involved) and four &dquo;incomplete&dquo; (weights derived directly from the factor structure in some intuitive manner) factor score types was used (Morris, 1979). A brief description is presented.…”

“…Using a computer-based Monte Carlo procedure parallel to that employed in a recent comparison of various types of factor scores (Morris, 1979) the investigator compared the double cross-validation replication predictive accuracies of six types of factor scores with that of full-rank data by utilizing a data set from the literature in which classroom achievement was predicted from affective and cognitive variables. Prediction accuracy was significantly more accurate for each of the six types of factor scores than for fullrank data.…”

Instructing First-Grade Children on Patterning Improves Reading and Mathematics

“…The achievement variables were reduced to two factors, mathematics and reading, by using a standard unit-weighted factor score (i.e., a composite score using standardized values; Morris, 1979). These scores tend to maintain the predictive validity found in standard exploratory factor analyses and improve the generalizability of the findings compared to differential weighting (Grice & Harris, 1998).…”