Premature conclusions about the signal-to-noise ratio in structural equation modeling research: A commentary on Yuan and Fang (2023)

In a recent article published in this journal, Yuan and Fang (British Journal of Mathematical and Statistical Psychology, 2023) suggest comparing structural equation modeling (SEM), also known as covariance-based SEM (CB-SEM), estimated by normal-distribution-based maximum likelihood (NML), to regression analysis with (weighted) composites estimated by least squares (LS) in terms of their signal-to-noise ratio (SNR). They summarize their findings in the statement that “[c]ontrary to the common belief that CB-SEM is the preferred method for the analysis of observational data, this article shows that regression analysis via weighted composites yields parameter estimates with much smaller standard errors, and thus corresponds to greater values of the [SNR].” In our commentary, we show that Yuan and Fang have made several incorrect assumptions and claims. Consequently, we recommend that empirical researchers not base their methodological choice regarding CB-SEM and regression analysis with composites on the findings of Yuan and Fang as these findings are premature and require further research.     

Shrinkage estimation of linear combinations of true scores

This paper is concerned with combining observed scores from sections of tests. It is demonstrated that in the presence of population information a linear combination of true scores can be estimated more efficiently than by the same linear combination of the observed scores. Three criteria for optimality are discussed, but they yield the same solution which can be described and motivated as a multivariate shrinkage estimator.Input from Eric Bradlow, Charles Lewis, and Linda Zeger is acknowledged. Research for this paper was funded by the Program Research Council (ETS). Suggestions of the Editor and of anonymous referees were instrumental in several improvements of the paper.     

The effect of additional variables on factor indeterminacy in models with a single common factor

Determinate solutions for the indeterminate common factor ofp variables satisfying the single common factor model are not unique. Therefore an infinite sequence of additional variables that conform jointly with the originalp variables to the original single common factor model does not determine a unique solution for the indeterminate factor of thep variables (although the solution is unique for the factor of the infinite sequence). Other infinite sequences may be found to determine different solutions for the factor of the originalp variables. The paper discusses a number of theorems about the effects of additional variables on factor indeterminacy in a model with a single common factor and draws conclusions from them for factor theory in general.     

On the base-free measure of change proposed by Tucker,Damarin and Messick

Tucker, Damarin and Messick proposed a base-free measure of change which involves the computation of residual scores that are uncorrelated with true scores on the pretest. The present note discusses this change measure and demonstrates that, because of an incorrect derivation by the authors, properties they attribute to (the coefficient for the regression of true scores from the second testing on true scores from the first testing) are, in fact, properties ofb, the ordinary regression coefficient. A correct derivation of the initial position—change correlation in terms of is obtained, and Tucker et al.'s discussion of the law of initial values is reconsidered.The preparation of this paper was supported by the Learning Research and Development Center supported in part as a research and development center by funds from the National Institute of Education.     

The effects of primary reward on the I.Q. performance of grade-school children as a function of initial I.Q. level

The effect of candy reward on I.Q. scores was investigated in 72 first- and second-grade children. All subjects were administered Form A of the Peabody Picture Vocabulary Test and, based upon these scores, were divided into three blocks: low, middle, and high. From each block, subjects were randomly assigned to one of three conditions (contingent reward, noncontingent reward, or no reward) that were in effect during administration of Form B. Results showed that candy given contingent upon each correct response increased I.Q. scores for the initially low scoring subjects, but had no influence on the scores of middle and high scoring subjects.     

Comments on “the measurement of factorial indeterminacy”

Guttman's index of indeterminacy (2² – 1) measures the potential amount of uncertainty in picking the right alternative interpretation for a factor. When alternative solutions for a factor are equally likely to be correct, then the squared multiple correlation ² for predicting the factor from the observed variables is the average correlation _AB between independently selected alternative solutionsA andB, while var ( _AB )=(1 – ²)²/s, wheres is the dimensionality of the space in which unpredicted components of alternative solutions are to be found. When alternative solutions for the factor are not equally likely to be chosen, ² is the lower bound for E( _AB ); however, E( _AB ) need not be a modal value in the distribution of _AB . Guttman's index and E( _AB ) measure different aspects of the same indeterminacy problem.     

The multiple meanings of secondary gain

The historical development of the concept of secondary gain is described in this article. Freud introduced this concept as a complement to primary gain. Freud modified the scope of both concepts during his career, but they remained within the boundary of an intrapsychological mechanism. Outside psychoanalysis, the concept of secondary gain has acquired further meaning with higher emphasis on interpersonal and social aspects. Consequently, it is often unclear what a writer or speaker means when he uses the term secondary gain. The different meanings of secondary gain in and outside psychoanalysis are illustrated with reference to literature and case reports.     

Potential underlying mechanisms for greater weight gain in massaged preterm infants

In this paper, potential underlying mechanisms for massage therapy effects on preterm infant weight gain are reviewed. Path analyses are presented suggesting that: (1) increased vagal activity was associated with (2) increased gastric motility, which, in turn, was related to (3) greater weight gain; and (4) increased IGF-1 was related to greater weight gain. The change in vagal activity during the massage explained 49% of the variance in the change in gastric activity. And, the change in vagal activity during the massage explained 62% of the variance in the change in insulin. That the change in gastric activity was not related to the change in insulin suggests two parallel pathways via which massage therapy leads to increased weight gain: (1) insulin release via the celiac branch of the vagus; and (2) increased gastric activity via the gastric branch of the vagus.     

Moderate versus light pressure massage therapy leads to greater weight gain in preterm infants

Sixty-eight preterm infants (M GA = 30 weeks) were randomly assigned to a moderate or to a light pressure massage therapy group to receive 15 massages three times per day for 5 days. Behavior state, stress behaviors and heart rate were recorded for 15 min before and during the first 15-min therapy session. Weight gain was recorded over the 5-day therapy period. The moderate versus light pressure massage group gained significantly more weight per day. During the behavior observations the moderate versus light pressure massage group showed significantly lower increases from the pre-session to the session recording on: (1) active sleep; (2) fussing; (3) crying; (4) movement; and (5) stress behavior (hiccupping). They also showed a smaller decrease in deep sleep, a greater decrease in heart rate and a greater increase in vagal tone. Thus, the moderate pressure massage therapy group appeared to be more relaxed and less aroused than the light pressure massage group which may have contributed to the greater weight gain of the moderate pressure massage therapy group.