Adherence in childhood diabetes: results of a confirmatory factor analysis

In an earlier study (Johnson, Silverstein, Rosenbloom, Carter, & Cunningham, 1986), an exploratory factor analysis identified five components of adherence in childhood diabetes. In this investigation, a simultaneous confirmatory analysis was used to test the equality of this factor pattern across two independent samples. Factors 1 through 4--Exercise, Injection, Diet Type, and Eating/Testing Frequency-were confirmed. Factor 5--Diet Amount--proved to be too complex; the adherence measures comprising this factor (total calories and concentrated sweets consumed) are best treated as separate, single-indicator constructs. The results support a multivariate conceptualization of adherence, offer insight into the nature of the components underlying diabetes adherence, and provide measurement information for reliable component estimation.     

FACTORIAL INVARIANCE OF BIOGRAPHICAL FACTORS

A biographical information blank (BIB) was administered to students in grades 7, 9, and 11, and was subsequently analyzed to determine the stability of both its factor pattern and structure. This was done by deriving a single average factor pattern matrix which was rotated to simple structure and then to similarity to each of three factor matrices at each grade level. Of 11 factors extracted, all but three showed reasonably good stability. Those factors that showed the greatest change, in terms of their presence over the three grade levels, were General Appreciation of School Courses, Social Activities, and High Level Literary Activities. Implications of stability in factor pattern and structure for further BIB development and for utilization in the framework of a longitudinal study are discussed.     

A note on invariance in three-mode factor analysis

Previous results of the application of Lawley's selection theorem to the common factor analysis model are extended to a revision of Tucker's three-mode principal components model. If the regression of the three-mode manifest variates on variates used to select subpopulations is both linear and homoscedastic, the two factor pattern matrices, the core matrix, and the residual variance-covariance matrix in the three-mode model can all be assumed to be invariant across subpopulations. The implication of this finding for simple structure is discussed.     

Dynamic estimation in the extended marginal Rasch model with an application to mathematical computer-adaptive practice

We introduce a general response model that allows for several simple restrictions, resulting in other models such as the extended Rasch model. For the extended Rasch model, a dynamic Bayesian estimation procedure is provided, which is able to deal with data sets that change over time, and possibly include many missing values. To ensure comparability over time, a data augmentation method is used, which provides an augmented person-by-item data matrix and reproduces the sufficient statistics of the complete data matrix. Hence, longitudinal comparisons can be easily made based on simple summaries, such as proportion correct, sum score, etc. As an illustration of the method, an example is provided using data from a computer-adaptive practice mathematical environment.     

Instrumental variables in factor analysis

The factor analysis model is rewritten as a system of linear structural relations with errors in variables. The method of instrumental variables is applied to this revised form of the model to obtain estimates of the factor loading matrix. The relation between this method and interbattery analysis, proportional profile analysis, and canonical factor analysis is pointed out. In addition, an estimation procedure based on replicated sampling different from proportional profile analysis is given.     

Regularized Finite Mixture Models for Probability Trajectories

Finite mixture models are widely used in the analysis of growth trajectory data to discover subgroups of individuals exhibiting similar patterns of behavior over time. In practice, trajectories are usually modeled as polynomials, which may fail to capture important features of the longitudinal pattern. Focusing on dichotomous response measures, we propose a likelihood penalization approach for parameter estimation that is able to capture a variety of nonlinear class mean trajectory shapes with higher precision than maximum likelihood estimates. We show how parameter estimation and inference for whether trajectories are time-invariant, linear time-varying, or nonlinear time-varying can be carried out for such models. To illustrate the method, we use simulation studies and data from a long-term longitudinal study of children at high risk for substance abuse. This work was supported in part by NIAAA grants R37 AA07065 and R01 AA12217 to RAZ.     

On the symmetric treatment of an asymmetric approach to factor analysis

On the assumption that a partitioning can be found such that three mutually exclusive test vector configurations span the same factor space, a procedure is derived whereby symmetric parts of the correlation matrix are estimated from functions of asymmetric parts treated symmetrically. This yields an explicit matrix formula for communality estimation which generalizes earlier work by Albert. Conventional factoring methods, with all their computational and fitting advantages, can be applied once the symmetric portions of the correlation matrix have been estimated. Extension to four subgroups of test vectors allows for a matrix generalization of the old tetrad difference criterion to the multiple-factor case.     

Exploratory second-order analyses for components and factors

Abstract: Exploratory methods using second‐order components and second‐order common factors were proposed. The second‐order components were obtained from the resolution of the correlation matrix of obliquely rotated first‐order principal components. The standard errors of the estimates of the second‐order component loadings were derived from an augmented information matrix with restrictions for the loadings and associated parameters. The second‐order factor analysis proposed was similar to the classical method in that the factor correlations among the first‐order factors were further resolved by the exploratory method of factor analysis. However, in this paper the second‐order factor loadings were estimated by the generalized least squares using the asymptotic variance‐covariance matrix for the first‐order factor correlations. The asymptotic standard errors for the estimates of the second‐order factor loadings were also derived. A numerical example was presented with simulated results.     

A NEW MATRIX FOR THE ASSESSMENT OF FACTOR CONTRIBUTIONS

The matrix product of the initial factor loading matrix times the least- squares orthonormal approximation to the general oblique transformation matrix is suggested to be the most adequate matrix for the evaluation of the contributions of factors to variables. This factor contribution matrix can also re- place the primary factor pattern matrix in evaluating oblique simple structure.     

Rotation to achieve factorial invariance

Under certain conditions it is reasonable to assume that the same factor pattern matrix will describe the regression of observed on factor scores in different populations. However, ordinary factoring procedures will not reveal in general the existence of such a factor pattern matrix. Two procedures for rotating any number of factor pattern matrices based on different populations to conform to a single best fitting factor pattern matrix are developed in this paper. It is assumed that the same number of factors have been determined for each population. Both procedures will yield oblique results in the various populations. The procedures are illustrated with data taken from the 1939 Holzinger-Swineford monograph. Four groups of individuals are utilized.     

MIRT模型中多维能力及其相关矩阵估计的影响因素

多维项目反应理论因其模型本身的天然优势及其兼具因素分析与项目反应理论于一身的优点,而被广大研究者及应用者所重视.本研究在前人研究基础上,重点讨论MIRT多维能力及能力间相关矩阵的参数估计问题.研究采用Monte Carlo模拟方法进行,在三因素完全随机设计（4 ×3×3）下,使用MCMC算法,探讨测验维度数、维度间的相关大小和测验项目数三个因素对MIRT能力及其相关矩阵估计的影响.     

Notes on factorial invariance

Lawley's selection theorem is applied to subpopulations derived from a parent in which the classical factor model holds for a specified set of variables. The results show that there exists an invariant factor pattern matrix that describes the regression of observed on factor variables in every subpopulation derivable by selection from the parent, given that selection does not occur directly on the observable variables and does not reduce the rank of the system. However, such a factor pattern matrix is not unique, which in turn implies that if a simple structure factor pattern matrix can be satisfactorily determined in one such subpopulation the same simple structure can be found in any subpopulation derivable by selection. The implications of these results for parallel proportional profiles and factor matching techniques are discussed.     

新世纪20年国内心理统计方法研究回顾

新世纪头20年, 国内心理学11本专业期刊一共发表了213篇统计方法研究论文。研究范围主要包括以下10类(按论文篇数排序)：结构方程模型、测验信度、中介效应、效应量与检验力、纵向研究、调节效应、探索性因子分析、潜在类别模型、共同方法偏差和多层线性模型。对各类做了简单的回顾与梳理。结果发现, 国内心理统计方法研究的广度和深度都不断增加, 研究热点在相互融合中共同发展; 但综述类论文比例较大, 原创性研究论文比例有待提高, 研究力量也有待加强。     

On Green's best linear composites with a specified structure,and oblique estimates of factor scores

Green solved the problem of least-squares estimation of several criteria subject to the constraint that the estimates have an arbitrary fixed covariance or correlation matrix. In the present paper an omission in Green's proof is discussed and resolved. Furthermore, it is shown that some recently published solutions for estimating oblique factor scores are special cases of Green's solution for the case of fixed covariance matrices.     

Organization and components of psychomotor ability

We investigated the organization and components of psychomotor abilities by administering a diverse set of cognitive and psychomotor tasks to a group of recent high school graduates (N = 161). Confirmatory factor analyses identified two psychomotor factors: a general factor associated with all psychomotor tests and an orthogonal psychomotor learning factor associated exclusively with practiced psychomotor tests. Path analyses suggested that the general psychomotor factor could be largely accounted for by two cognitive factors, general working-memory capacity (r = .67) and an orthogonal time estimation factor (r = .32). Most of the psychomotor learning factor variance was unique, but psychomotor learning was somewhat related to processing speed (r = .49). We conclude that initial psychomotor performance is constrained by working-memory limits and the ability to keep track of time. Practiced psychomotor skill is additionally limited by processing speed, consistent with the literature on the development of process automaticity. The Discussion addresses (a) the small dimensionality of the psychomotor abilities space, (b) our discovery of the importance of time estimation and other cognitive factors in psychomotor learning, and (c) the changing nature of psychomotor skill with practice.     

Estimation of maximal reliability for multiple‐component instruments in multilevel designs

A procedure for point and interval estimation of maximal reliability of multiple‐component measuring instruments in multi‐level settings is outlined. The approach is applicable to hierarchical designs in which individuals are nested within higher‐order units and exhibit possibly related performance on components of a given homogeneous scale. The method is developed within the framework of multi‐level factor analysis. The proposed procedure is illustrated with an empirical example.     

Bias in longitudinal data analysis with missing data using typical linear mixed‐effects modelling and pattern‐mixture approach: An analytical illustration

We analytically derive the fixed‐effects estimates in unconditional linear growth curve models by typical linear mixed‐effects modelling (TLME) and by a pattern‐mixture (PM) approach with random‐slope‐dependent two‐missing‐pattern missing not at random (MNAR) longitudinal data. Results showed that when the missingness mechanism is random‐slope‐dependent MNAR, TLME estimates of both the mean intercept and mean slope are biased because of incorrect weights used in the estimation. More specifically, the estimate of the mean slope is biased towards the mean slope for completers, whereas the estimate of the mean intercept is biased towards the opposite direction as compared to the estimate of the mean slope. We also discuss why the PM approach can provide unbiased fixed‐effects estimates for random‐coefficients‐dependent MNAR data but does not work well for missing at random or outcome‐dependent MNAR data. A small simulation study was conducted to illustrate the results and to compare results from TLME and PM. Results from an empirical data analysis showed that the conceptual finding can be generalized to other real conditions even when some assumptions for the analytical derivation cannot be met. Implications from the analytical and empirical results were discussed and sensitivity analysis was suggested for longitudinal data analysis with missing data.     

Some relations between guttman's principal components of scale analysis and other psychometric theory

Guttman's principal components for the weighting system are the item scoring weights that maximize the generalized Kuder-Richardson reliability coefficient. The principal component for any item is effectively the same as the factor loading of the item divided by the item standard deviation, the factor loadings being obtained from an ordinary factor analysis of the item intercorrelation matrix.