An Application of the LC-LSTM Framework to the Self-esteem Instability Case

The present research evaluates the stability of self-esteem as assessed by a daily version of the Rosenberg (Society and the adolescent self-image, Princeton University Press, Princeton, 1965) general self-esteem scale (RGSE). The scale was administered to 391 undergraduates for five consecutive days. The longitudinal data were analyzed using the integrated LC-LSTM framework that allowed us to evaluate: (1) the measurement invariance of the RGSE, (2) its stability and change across the 5-day assessment period, (3) the amount of variance attributable to stable and transitory latent factors, and (4) the criterion-related validity of these factors. Results provided evidence for measurement invariance, mean-level stability, and rank-order stability of daily self-esteem. Latent state-trait analyses revealed that variances in scores of the RGSE can be decomposed into six components: stable self-esteem (40 %), ephemeral (or temporal-state) variance (36 %), stable negative method variance (9 %), stable positive method variance (4 %), specific variance (1 %) and random error variance (10 %). Moreover, latent factors associated with daily self-esteem were associated with measures of depression, implicit self-esteem, and grade point average.     

The analysis of variance and pairwise scaling

Variance analyses are presented for two data layouts—each corresponding to the class of all ordered pairs from a single finite set. The analysis of the dominance layout is in terms of a fixed effects linear model which includes parameters representing the scale values of the elements of the set, response bias, and pairwise interactions. A parallel parametrization is carried out for the composition layout for which corresponding point estimates and hypothesis tests are given. A joint treatment of concurrently observed dominance and composition layouts is suggested and illustrative data are presented.This research was supported in part by National Institutes of Health Grant MH-04439-06. The author would like to express his appreciation to Richard Beatty of the University of Toronto, James Baker and William Carroll of Oregon Research Institute, and J. E. Keith Smith of the University of Michigan, for their helpful comments concerning aspects of this work. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by NIH Grant FR-3.     

A course in the theory of mental tests

An outline for a course in test theory is presented, together with a list of assignments, problems, and a bibliography. The course has been given in the Psychology Department of the University of Chicago. The material is presented in outline form at the present time because of the increased need for training in test theory due to the increase in the use of psychological tests for classification of military personnel, and because much of the material in such a course must be selected from a wide array of articles in the literature. This material is presented in order that an organized body of material for instructional purposes may be readily available to those interested.On leave from the University of Chicago for a government research project at the College Entrance Examination Board, Princeton, New Jersey.     

F tests for the absolute invariance of dominance and composition scales

Significance tests are developed for evaluating the absolute invariance of the dominance and composition scales presented in a previous paper [Bechtel, 1967]. These tests derive from the multivariate normality of the estimated scale values—this multinormality stemming from that of the observations upon which these estimated scale parameters are based. The scales compared by means of the present techniques will typically be constructed under distinct experimental conditions, which may take the concrete form of treatments, occasions, individuals, or groups. Thus the present tests possess a wide range of applicability including various experimental designs in which scale configuration is the dependent variable. Illustrative data are used in statistically comparing the scale structures of two different individuals.This research was supported in part by National Institutes of Health Grant MH-04439-06. The author would like to express his appreciation to Fred C. Andrews of the University of Oregon and J. E. Keith Smith of the University of Michigan for their helpful comments concerning aspects of this work. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by NIH Grant FR-3.     

Effects of Modeling the Heterogeneity on Inferences Drawn from Multilevel Designs

This article uses Monte Carlo techniques to examine the effect of heterogeneity of variance in multilevel analyses in terms of relative bias, coverage probability, and root mean square error (RMSE). For all simulated data sets, the parameters were estimated using the restricted maximum-likelihood (REML) method both assuming homogeneity and incorporating heterogeneity into multilevel models. We find that (a) the estimates for the fixed parameters are unbiased, but the associated standard errors are frequently biased when heterogeneity is ignored; by contrast, the standard errors of the fixed effects are almost always accurate when heterogeneity is considered; (b) the estimates for the random parameters are slightly overestimated; (c) both the homogeneous and heterogeneous models produce standard errors of the variance component estimates that are underestimated; however, taking heterogeneity into account, the REML-estimations give correct estimates of the standard errors at the lowest level and lead to less underestimated standard errors at the highest level; and (d) from the RMSE point of view, REML accounting for heterogeneity outperforms REML assuming homogeneity; a considerable improvement has been particularly detected for the fixed parameters. Based on this, we conclude that the solution presented can be uniformly adopted. We illustrate the process using a real dataset.     

An estimation of true scores in the case of items scored on a continuous scale

For the tests in which the score on an item is not restricted to 0 and 1, but is any number on a continuous scale, a procedure for estimating an examinee's true score is given. For the case of 0, 1 item scoring this problem was considered by Lord [1959]. Following Lord, the least squares estimation procedure is used and the regression coefficient is obtained, which is compared with the generalized KR(20) and KR(21) formulas. Also, results are discussed using analysis of variance models.Now at Brooklyn College of the City University of New York.     

Analytic smoothing for equipercentile equating under the common item nonequivalent populations design

A cubic spline method for smoothing equipercentile equating relationships under the common item nonequivalent populations design is described. Statistical techniques based on bootstrap estimation are presented that are designed to aid in choosing an equating method/degree of smoothing. These include: (a) asymptotic significance tests that compare no equating and linear equating to equipercentile equating; (b) a scheme for estimating total equating error and for dividing total estimated error into systematic and random components. The smoothing technique and statistical procedures are explored and illustrated using data from forms of a professional certification test.     

Matrix analysis of identifiability of some finite markov models

Methods developed by Bernbach [1966] and Millward [1969] permit increased generality in analyses of identifiability. Matrix equations are presented that solve part of the identifiability problem for a class of Markov models. Results of several earlier analyses are shown to involve special cases of the equations developed here. And it is shown that a general four-state chain has the same parameter space as an all-or-none model if and only if its representation with an observable absorbing state is lumpable into a Markov chain with three states.This research was supported by the U.S. Public Health Service under Grant MH-12717 to Indiana University and Grant GM-1231 to the University of Michigan.Now at the University of Texas, Austin.     

Empirically derived groups in the assessment of recovery from aphasia.

This paper examines the pretreatment intercorrelation matrix of the subtests of the Porch Index of Communication Ability to derive factors reflecting components of language impairment. In addition to a general factor reflecting overall language dysfunction, five specific factors reflecting verbal competency (fluency), graphic-verbal expression, gestural-verbal expression, gestural-nonverbal comprehension, and graphic-geometric comprehension were found which accounted for 90.6% of the total variance. A cluster analysis of the five pretreatment factor scores yielded six groups which accounted for 79% of the variance for these factors. These groups were differentiated primarily in terms of impairment and showed a high rate of accuracy prediction for group membership (97.5%). These groups were extremely stable, as shown by the 75% accurate prediction rate derived from the post-treatment factor scores. The effectiveness of this model in generating homogeneous and highly discriminable groups based on objective measures of the patient's language functions indicates that classification of patients into empirical groups should be a major concern of any research design. Implications for assessing effectiveness of therapeutic intervention and the design of test battery were also discussed.     

Function invariant and parameter scale-free transformation methods

The parameter matrices of factor analysis and principal component analysis are arbitrary with respect to the scale of the factors or components; typically, the scale is fixed so that the factors have unit variance. Oblique transformations to optimize an objective statement of a principle such as simple structure or factor simplicity yield arbitrary solutions, unless the criterion function is invariant with respect to the scale of the factors, or the parameter matrix is scale free with respect to the factors. Criterion functions that are factor scale-free have a number of invariance characteristics, such as being equally applicable to primary pattern or reference structure matrices. A scale-invariant simple structure function of previously studied function components is defined. First and second partial derivatives are obtained, and Newton-Raphson iterations are utilized. The resulting solutions are locally optimal and subjectively pleasing.Aspects of this paper were presented at the 1970 and 1974 annual meetings, Society of Multivariate Experimental Psychology, and the 1975 annual meeting, Psychometric Society. This investigation was supported in part by a Research Scientist Development Award (K02-DA00017) and research grants (MH24149 and DA01070) from the U. S. Public Health Service. The assistance of Bonnie Barron, Sik-Yum Lee, and several extremely helpful reviewers is gratefully acknowledged.     

Relation between speed of reaction and psychometric tests of mental ability in musculoskeletal injury-prone subjects

Long reaction time (RT), long choice reaction time (CRT), and low scores on psychometric tests of mental ability (MA) have in previous studies been related to musculoskeletal injuries. There has been controversy concerning the relation between slow reaction and low-grade MA recently, the old hypothesis of negative correlation between RT and MA being discussed. The aim of this study was to analyze the relation between speed of reaction and MA. For a sample of 123 volunteer healthy young men simple RT, choice RT, and spatial (block design), verbal and arithmetic components of MA were tested. A principal component analysis was performed and the factor matrix was rotated orthogonally using the varimax method. Two factors were extracted accounting for 73% of the total variance in data space. The mental ability factor, which was responsible for 70% of the variance in factor space, was comprised of components of MA and choice RT. The speed of reaction factor accounted for the remaining 30% of the variance in factor space and was comprised of simple and choice RTs. As choice RT had significant loading on the mental ability factor, the subjects having scores in the lowest quartile on both choice RT and MA total score were compared with the independent expected value by using the chi-squared test. The results of low-grade MA and slow choice reaction were not independent. Accordingly, the results do not support the entire distinction between traditional mental ability or convergent thinking and speed of reaction in normal subjects.(ABSTRACT TRUNCATED AT 250 WORDS)     

Estimation of true score and error variance for tests under various equivalence assumptions

Maximum-likelihood estimators of true score variance and error variance for mental tests are derived for six different models of equivalent measurements. Statistical properties of the estimators are examined. Main emphasis is placed upon essentially-equivalent measurements. A statistical criterion for this type of measurement is given. The solution of the comparatively simple maximum-likelihood equations is effected by means of a rapid Newton-Raphson procedure. Two different initial estimators are considered and their relative merits in terms of second moments evaluated. Four numerical examples are appended by way of illustration.Paper read at the Mathematical Psychology Meeting, August 28, 1968, at Stanford, Calfornia.This research was supported in part by the National Institute of Child Health and Human Development, Research Grant 1 P01 HD01762.     

USING RANDOM RATHER THAN FIXED EFFECTS MODELS IN META-ANALYSIS: IMPLICATIONS FOR SITUATIONAL SPECIFICITY AND VALIDITY GENERALIZATION

Combining statistical information across studies (i.e., meta-analysis) is a standard research tool in applied psychology. The most common meta-analytic approach in applied psychology, the fixed effects approach, assumes that individual studies are homogeneous and are sampled from the same population. This model assumes that sampling error alone explains the majority of observed differences in study effect sizes and its use has lead some to challenge the notion of situational specificity in favor of validity generalization. We critique the fixed effects methodology and propose an advancement–the random effects model (RE) which provides estimates of how between-study differences influence the relationships under study. RE models assume that studies are heterogeneous since they are often conducted by different investigators under different settings. Parameter estimates of both models are compared and evidence in favor of the random effects approach is presented. We argue against use of the fixed effects model because it may lead to misleading conclusions about situational specificity.     

Sex differences in impulsivity and intellectual ability

Literature on sex differences in impulsivity has tended to focus on differences between groups, while ignoring relationships beyond zero order correlations. The purpose of this study was to evaluate Maccoby's hypothesis (1966) of opposite-direction correlations where the relationship between a set of variables (e.g., impulsivity and intellectual ability) is curvilinear, with males and females being systematically distributed on opposite sides of the curve. The Primary Mental Abilities (PMA) and Matching Familiar Figures tests were administered to 44 males and 49 females. The relationship between all of the PMA subtests and impulsivity was curvilinear for males, but linear for females on all but one of the subtests. The importance and implications of examining distribution differences rather than group differences are discussed.Support for this study has come from the Office of Research Administration, University of Kansas, Grant Number 3581-5038. This paper was presented in part at the meeting of the American Psychological Association, Chicago, August 1975, Division 7.     

Two learning models for responses measured on a continuous scale

Two linear operator models are presented for a class of learning situations in which the response is on a numerical scale and the subject is given the magnitude of his error on some or all of the trials. Theoretical expressions are developed for sequential dependencies, mean learning curves, variances, and covariances, which permit a number of tests of goodness of fit.This work was supported by Grant G-12986 from the National Science Foundation. The author wishes to express his appreciation to J. H. Alexander for his cogent assistance.     

Model Selection with the Linear Mixed Model for Longitudinal Data

Model building or model selection with linear mixed models (LMMs) is complicated by the presence of both fixed effects and random effects. The fixed effects structure and random effects structure are codependent, so selection of one influences the other. Most presentations of LMM in psychology and education are based on a multilevel or hierarchical approach in which the variance-covariance matrix of the random effects is assumed to be positive definite with nonzero values for the variances. When the number of fixed effects and random effects is unknown, the predominant approach to model building is a step-up method in which one starts with a limited model (e.g., few fixed and random intercepts) and then additional fixed effects and random effects are added based on statistical tests. A model building approach that has received less attention in psychology and education is a top-down method. In the top-down method, the initial model has a single random intercept but is loaded with fixed effects (also known as an “overelaborate” model). Based on the overelaborate fixed effects model, the need for additional random effects is determined. There has been little if any examination of the ability of these methods to identify a true population model (i.e., identifying the model that generated the data). The purpose of this article is to examine the performance of the step-up and top-down model building approaches for exploratory longitudinal data analysis. Student achievement data sets from the Chicago longitudinal study serve as the populations in the simulations.     

Canonical analyses of mental test profiles

HÄrnqvist, K. Canonical analyses of mental test profiles. Scand. J. Psychol., 1973, 14, 282–290.-The one-year stability of profiles of mental test scores from four PMA factors was studied in grades 4 through 9 (ages 11 to 16) by means of canonical correlations and estimates of "redundancy" between batteries. Change in test content within the framework of the same PMA factors meant a greater decrease in profile similarity than change in time for parallel content. The same components were needed for explaining the variance common to two batteries of tests with a year's interval as to batteries of simultaneous tests. In the discussion the present approach is related to other methods for studying profile similarity, profile reliability and profile change.     

The impact of omitting the interaction between crossed factors in cross‐classified random effects modelling

Cross‐classified random effects modelling (CCREM) is a special case of multi‐level modelling where the units of one level are nested within two cross‐classified factors. Typically, CCREM analyses omit the random interaction effect of the cross‐classified factors. We investigate the impact of the omission of the interaction effect on parameter estimates and standard errors. Results from a Monte Carlo simulation study indicate that, for fixed effects, both coefficients estimates and accompanied standard error estimates are not biased. For random effects, results are affected at level 2 but not at level 1 by the presence of an interaction variance and/or a correlation between the residual of level two factors. Results from the analysis of the Early Childhood Longitudinal Study and the National Educational Longitudinal Study agree with those obtained from simulated data. We recommend that researchers attempt to include interaction effects of cross‐classified factors in their models.     

African American women's sexual satisfaction as a dimension of their sex roles

African American women's sexual satisfaction in heterosexual relationships was examined as a dimension of their sex roles. Responses to questions about sexual behaviors and interactions they preferred in primary relationships were selected from a larger study of a stratified random sample of 126 African American women. Three factors were identified: sexual responsiveness, sexual expression, and sexual interest and enthusiasm. The factors are described as profiles that may enhance or limit women's male-female sexual relationships. The implications of African American women's sexual satisfaction as an important dimension to understand in today's AIDS related sexual climate is discussed within a socio-cultural context.A modified version of this paper was presented at the American Anthropological Association, November 1987, Chicago, Illinois. The research was funded by The Center for Prevention and Control of Rape, NIMH Grant, R01 MH33603 and through a Research Scientist Career Development Award to the first author, K01 MH00269.     

无铆题情况下测验分数等值方法探索——构造铆测验法

研究旨在探索无铆题情况下,使用构造铆测验法,实现测验分数等值。研究一和研究二分别探索题目难度排序错误、铆题难度差异对构造铆测验法的影响。结果表明：（1）等组条件下,随着错误铆题比例,难度排序错误程度,铆题难度差异增大,构造铆测验法的等值误差逐渐增大,随机等组法的等值误差较为稳定;不等组条件下,构造铆测验法的等值误差均小于随机等组法;（2）对于构造铆测验法,在不等组条件下,铆测验长度越短,等值误差越大。