A comparison of four methods of constructing factor scores

Four least-squares methods for constructing factor scores have been described in the literature. The formal properties of these scores are developed, and they are compared in terms of four generally desirable properties of constructed factor scores. In particular, it is shown that two of the methods yield scores that are conditionally unbiassed, and univocal in the sense of Guilford and Michael, though not orthogonal, while one of the other methods yields orthogonal scores.It is shown that constructed factor scores cannot be simultaneously univocal and orthogonal, unless we choose the special basis in factor space given by Canonical Factor Analysis.The general problem of choosing between the methods is discussed, on the basis of the theoretical relations obtained.EDITOR'S NOTE: The reader will quickly discover that this article develops several of the generalizations given in the second part of the preceding article, On Factors and Factor Scores. Independent development of the same generalizations is, of course, not a new phenomenon. Because the Presidential Address automatically is accepted for publication and given space in the December issue, it was decided that the only fair thing to do was to print this article in the same issue.     

Relational perception and modes of perceiver operation

Judgments were made of the size of a small, luminous (inner) square appearing in the center of a somewhat larger, variable (outer) square, the whole pattern appearing in the dark. Accuracy of judgment was greatest when the outer square was constant from trial to trial but deteriorated when the outer square also varied in size, reaching a lower limit less than the accuracy produced under the absolute judgment condition (no outer square presented). An application of multiple discriminant analysis and the use of a maximum likelihood observer model provided estimates of the extent to which Os responded to inner and outer size variation as separate aspects of stimulation. Although Os differed markedly in this respect, their ability to identify inner square size under the various conditions did not reflect this difference.     

The effect of encoding training on perceptual recall

The effect of encoding training on tachistoscopic performance was measured by training groups of Ss in either an octal or a standardized English encoding of nine place binary numbers. A control group of Ss was allowed to encode ad lib during an equivalent training period. Performance was measured before, during and after the encoding training. It was found that imposing a code on S impaired tachistoscopic performance both during and for some time after the encoding training. Possible reasons for this effect are discussed.