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.     

Effects of active student response during error correction on the acquisition and maintenance of geography facts by elementary students with learning disabilities

An alternating treatments design was used to compare the effects of Active Student Response (ASR) error correction and No Response (NR) error correction during instruction of the capitals of states and countries. Three students with learning disabilities were provided one-to-one daily instruction on four sets of 14 unknown capitals (7 ASR capitals and 7 NR capitals). Student errors during instruction on ASR capitals were immediately followed by the teacher stating the capital and the student repeating it (an active student response). Errors on NR capitals were immediately followed by the teacher stating the capital while the student visually attended to a geography card with the correct capital handwritten on it (an on-task response). During instruction each of the three students correctly stated more capitals taught with ASR instruction than he or she stated with NR error correction. Results of same-day and next-day tests show that all three students learned more capitals with ASR error correction than with NR error correction The students also correctly stated more ASR error correction capitals on 1-week maintenance tests.     

Inattention-Hyperactivity and Reading Achievement in Children from Low-Income Families: A Longitudinal Model

This study examined how preschool inattention-hyperactivity is related to elementary school reading achievement. Prereading skills were hypothesized to be a link between them. This link was explored using longitudinal data on 105 low-socioeconomic-status (SES) children's inattentive-hyperactive behavior and prereading skills in Head Start and in kindergarten and their inattentive-hyperactive behavior and reading skills in first grade. A model of this relationship was tested using structural equation modeling. The results failed to show a significant path between inattention-hyperactivity and prereading skills at both the Head Start and kindergarten levels. A significant path was found between first grade inattention-hyperactivity and reading skills, confirming that the strong relationship between inattention-hyperactivity and poor reading achievement commonly found in children from other SES levels was also significant in this low-SES sample. Strong relationships were found between pre-reading skills and reading skills, as well as among hyperactivity levels at the three grades. The issue of the direction of the path of influence between attention-behavior and reading achievement is addressed briefly; however, the results indicate that further longitudinal work is necessary to resolve this issue.     

A Comparison of Active Student Response and On-Task Instruction on the Acquisition and Maintenance of Health Facts by Fourth Grade Special Education Students

An alternating treatments design was used to compare the effects of active student response (ASR) and on-task (OT) instruction on the acquisition and maintenance of health facts during small-group lessons. Five students with learning difficulties (4 students identified as developmentally handicapped and 1 student identified as learning disabled) participated in daily instruction on weekly sets of 20 unknown health facts (10 facts assigned to the ASR condition and 10 to the OT condition). During ASR instruction, the teacher modeled the correct response to a health question that was presented visually on a health fact card, and the students immediately repeated the correct response in unison three times. During OT instruction, students attended visually to the health fact card as the teacher modeled the correct response. All 5 students made more correct responses on end-of-day tests on health facts taught with ASR instruction than they did on health facts taught with OT instruction. ASR instruction also produced consistently superior results on maintenance tests administered 2 weeks after instruction.     

Isotonic ordinal probabilistic models (ISOP)

The concept of an ordinal instrumental probabilistic comparison is introduced. It relies on an ordinal scale given a priori and on the concept of stochastic dominance. It is used to define a weakly independently ordered system, or isotonic ordinal probabilistic (ISOP) model, which allows the construction of separate sample-free ordinal scales on a set of subjects and a set of items. The ISOP-model is a common nonparametric theoretical structure for unidimensional models for quantitative, ordinal and dichotomous variables.Fundamental theorems on dichotomous and polytomous weakly independently ordered systems are derived. It is shown that the raw score system has the same formal properties as the latent system, and therefore the latter can be tested at the observed empirical level.I wish to thank 3 reviewers and 2 editors who contributed a lot to the readability and precision of the article.     

人格结构的动态分析

为了动态化地分析人格的结构。研究一采用个体性自由命名描述法考察人格的动态内容。１５０名大学生分别用１０个词描述实际的自我、理想的自我、应该的自我。词频统计反映了不同自我的内容特点。研究二采用常模化限定性描述法考察人格的结构特点,用研究珠高频词制成实际、理想、应该的自我词表。２００名大学生用７点量表分别评定各词表中的每个词适合描述相应的自我的程度。结果表明,实际的自我有５个因素,解释４７．１％的变异     

TRAINING PRESCHOOL CHILDREN TO RECRUIT NATURAL COMMUNITIES OF REINFORCEMENT1

Four normal and four deviant children aged four-to-six years were taught to judge the quality of their academic work in a preschool classroom, and to prompt or cue their teachers to comment about the quality of that work. When these skills did not generalize spontaneously to other teachers in concurrent natural situations, generalized responding was taught by the experimenter, in multiple-baseline design across subjects. This generalization programming enabled the children to contact a sometimes dormant, but readily available natural community of teacher praise and reinforcement, i.e., to recruit an increase in cued praise and schedules of praise for their good work. These behaviors may be important to young children who find themselves bereft of attention in classrooms.     

A stochastic model for test-retest correlations

A simple stochastic model is formulated in order to determine the optimal time between the first test and the second test when the test-retest method of assessing reliability is used. A forgetting process and a change in true score process are postulated. The optimal time between tests is derived by maximizing the probability that the respondent has not remembered the response on the first test and has not had a change in true score. The resulting test-retest correlation is then found to be a linear function of the true reliability of the test, where the slope of this function is the key probability of not remembering and having no change in true score. Some numerical examples and suggestions for using the results in empirical studies are given. Specific recommendations are presented for improved design and analysis of intentions data.This research was made possible by a grant from the Center for Food Policy Research, Graduate School of Business, Columbia University, New York, New York, 10027.     

Two simple classes of mastery scores based on the beta-binomial model

Two simple classes of mastery scores which are suitable for hand calculations are presented for beta-binomial test score distributions combined with linear and cubic referral success. The models provide a simple way to explore the consequences of selecting an arbitrary mastery score. Such assessment would be useful whenever the test user is not willing to posta priori a loss ratio, but wishes to look at the various consequences before aiming at a particular score.     

A comparison of the key-peck and treadle-press operants in the pigeon: differential-reinforcement-of-low-rate schedule of reinforcement

Key pecking and treadle pressing in pigeons were compared under concurrent (key-treadle) and single-operant differential-reinforcement-of-low-rate schedules of food reinforcement ranging from 5 to 60 sec (concurrent procedure) or 5 to 120 sec (single-operant procedure). Under both procedures, the two operants followed the same general law: decreasing response rate and reinforcement rate and increasing number of responses per reinforcement as a function of increasing schedule interval. High correlations were found between key pecking and treadle pressing for the measures of response rate, reinforcement rate, and responses per reinforcement. Regression equations allowed the prediction of treadle pressing from key pecking. More bursting occurred in responding to the key, and key pecking showed a more precise temporal discrimination than treadle pressing. A test for sequential dependencies between key and treadle responses showed significant dependencies not only under the concurrent procedure but also in data created artificially by merging key and treadle sequences from different pigeons under the concurrent procedure and from the same pigeon under the single-operant procedure. It seems likely that the sequential dependencies found were due to the independent action of the schedule on each operant and that behavioral dependencies did not occur with the concurrent training procedure. The key-peck operant does not appear to have any special qualities that preclude its use in discovering general laws of behavior, at least under the differential-reinforcement-of-low-rate schedule. The usefulness of the key peck in other situations requires direct experimental study.