Latent curve analysis

As a method for representing development, latent trait theory is presented in terms of a statistical model containing individual parameters and a structure on both the first and second moments of the random variables reflecting growth. Maximum likelihood parameter estimates and associated asymptotic tests follow directly. These procedures may be viewed as an alternative to standard repeated measures ANOVA and to first-order auto-regressive methods. As formulated, the model encompasses cohort sequential designs and allow for period or practice effects. A numerical illustration using data initially collected by Nesselroade and Baltes is presented.The authors wish to thank John Nesselroade for providing us the data for our illustration and Karen Paul and Connie Tilse for assisting in the data analysis. This research was supported by a grant (No. AG03164) from the National Institute on Aging to the senior author.     

Canonical analysis of longitudinal and repeated measures data with stationary weights

When measuring the same variables on different occasions, two procedures for canonical analysis with stationary compositing weights are developed. The first, SUMCOV, maximizes the sum of the covariances of the canonical variates subject to norming constraints. The second, COLLIN, maximizes the largest root of the covariances of the canonical variates subject to norming constraints. A characterization theorem establishes a model building approach. Both methods are extended to allow for Cohort Sequential Designs. Finally a numerical illustration utilizing Nesselroade and Baltes data is presented.The authors wish to thank John Nesselroade for permitting us to use the data whose analysis we present.     

Component analysis in cross-sectional and longitudinal data

An extension of component analysis to longitudinal or cross-sectional data is presented. In this method, components are derived under the restriction of invariant and/or stationary compositing weights. Optimal compositing weights are found numerically. The method can be generalized to allow differential weighting of the observed variables in deriving the component solution. Some choices of weightings are discussed. An illustration of the method using real data is presented.Preparation of this article was supported in part by PSC-CUNY Grant #665365 to Roger E. Millsap and by National Institute of Aging Grant NIA-AG03164-03 to William Meredith. The authors thank John Nesselroade for permitting the use of the data presented in the article.     

Improving Psychological Measurement: Does It Make a Difference? A Comment on Nesselroade and Molenaar (2016)

Nesselroade and Molenaar advocate the use of an idiographic filter approach. This is a fixed-effects approach, which may limit the number of individuals that can be simultaneously modeled, and it is not clear how to model the presence of subpopulations. Most important, Nesselroade and Molenaar's proposal appears to be best suited for modeling long time series on a few variables for a few individuals. Long time series are not common in psychological applications. Can it be applied to the usual longitudinal data we face? These are characterized by short time series (four to five points in time), hundreds of individuals, and dozens of variables. If so, what do we gain? Applied settings most often involve between-individual decisions. I conjecture that their approach will not outperform common, simpler, methods. However, when intraindividual decisions are involved, their approach may have an edge.     

Consistent Treatment of Variables and Causation Poses a Challenge for Behavioral Research Methods: A Commentary on Nesselroade and Molenaar (2016)

Nesselroade and Molenaar presented the ideographic filter as a proposal for analyzing lawful regularities in behavioral research. The proposal highlights an inconsistency that poses a challenge for behavioral research more generally. One can distinguish a broadly Humean approach from a broadly non-Humean approach as they relate to variables and to causation. Nesselroade and Molenaar rejected a Humean approach to latent variables that characterizes them as nothing more than summaries of their manifest indicators. By contrast, they tacitly accepted a Humean approach to causes characterized as nothing more than summaries of their manifest causal effects. A non-Humean treatment of variables coupled with a Humean treatment of causation creates a theoretical tension within their proposal. For example, one can interpret the same model elements as simultaneously representing both variables and causes. Future refinement of the ideographic filter proposal to address this tension could follow any of a number of strategies.     

Multilevel models in developmental psychological research: Rationales and applications

The armoury of statistical techniques has recently been enhanced with the multilevel model for longitudinal data. The present article explains the multilevel model for longitudinal data to the statistically non-sophisticated reader. It shows how the model relates to the five rationales of longitudinal research, as they were put forward by Baltes and Nesselroade (1979). In addition, it shows how the model matches Wohlwill's methodology of developmental functions. To elucidate the model further, three applications are given. The applications pertain to the development of children's sleeping duration during the first 18 months of life, the effects of early hospitalization on the daily frequency of crying, and the developmental relationship between social and solitary play.     

P-technique factor analyses of the Multiple Affect Adjective Check List (MAACL)

The Multiple Affect Adjective Check List (MAACL) has been found to have five first-order factors representing Anxiety, Depression, Hostility, Positive Affect, and Sensation Seeking and two second-order factors representing Positive Affect and Sensation Seeking (PASS) and Dysphoria. The present study examines whether these first- and second-order conceptions of affect (based on R-technique factor analysis) can also account for patterns of intraindividual variability in affect (based on P-technique factor analysis) in eight elderly women. Although the hypothesized five-factor model of affect was not testable in all of the present P-technique datasets, the results were consistent with this interindividual model of affect. Moreover, evidence of second-order (PASS and Dysphoria) and third-order (generalized distress) factors was found in one data set. Sufficient convergence in findings between the present P-technique research and prior R-technique research suggests that the MAACL is robust in describing both inter- and intraindividual components of affect in elderly women.This paper is based on the doctoral research of the first author and was partially supported by the National Institute of Aging Grant T32 AC 00048-12 to The Pennsylvania State University and a Grant-in-Aid of Research from Sigma Xi, The Scientific Research Society. The authors wish to thank John R. Nesselroade for his helpful comments on an early draft of this paper.     

A Note on the Conversion of Item Parameters Standard Errors

The relations among alternative parameterizations of the binary factor analysis (FA) model and two-parameter logistic (2PL) item response theory (IRT) model have been thoroughly discussed in literature. However, the conversion formulas widely available are mainly for transforming parameter estimates from one parameterization to another. There is a lack of discussion about the standard error (SE) conversion among different parameterizations, when SEs of IRT model parameters are often of immediate interest to practitioners. This article provides general formulas for computing the SEs of transformed parameter values, when these parameters are transformed from FA to IRT models. These formulas are suitable for unidimensional 2PL, multidimensional 2PL, and bi-factor 2PL models. A simulation study is conducted to verify the formula by providing empirical evidence. A real data example is given in the end for an illustration.     

Alternative approaches to factorial invariance

Special cases of the factor analysis model are developed for four selection situations. Methods are suggested whereby parameters in each case can be estimated using a maximum likelihood procedure recently developed by Jöreskog. Also, a numerical illustration is presented for each case.This research was supported by a grant from the University Research Council, Vanderbilt University.     

On the equivalence of two oblique congruence rotation methods,and orthogonal approximations

Tucker's method of oblique congruence rotation is shown to be equivalent to a procedure by Meredith. This implies that Monte Carlo studies on congruence by Nesselroade, Baltes and Labouvie and by Korth and Tucker are highly comparable. The problem of rotating two matrices orthogonally to maximal congruence has not yet been solved. An approximate solution to this problem can be derived from Tucker's method. Even better results can be obtained from a Procrustes rotation followed by rotation to simple structure.     

Illustrating a mixed-method approach for validating culturally specific constructs

The purpose of this article is to illustrate a mixed-method approach (i.e., combining qualitative and quantitative methods) for advancing the study of construct validation in cross-cultural research. The article offers a detailed illustration of the approach using the responses 612 Sri Lankan adolescents provided to an ethnographic survey. Such surveys offer a connection between the primary methodologies used (i.e., ethnographic and factor analytic approaches) as they are predicated on qualitative inquiry and allow for the application of factor analysis. If the qualitatively derived constructs are comparable to factor analytic results, then triangulation across methods is achieved and a survey can be developed that is sensitive to culturally specific phenomena. The illustration of this approach uses data from an ethnographic survey of self-concept, as defined by Harter (1999) [Harter, S. (1999). The construction of the self: A developmental perspective. New York: The Guilford Press]. The construction of the self: A developmental perspective. New York: The Guilford Press]. The overall finding is that three constructs emerged from the factor analysis and were reconciled with the ethnographic data.     

Ant Colony Optimization and Local Weighted Structural Equation Modeling. A Tutorial on Novel Item and Person Sampling Procedures for Personality Research

Measurement in personality development faces many psychometric problems. First, theory‐based measurement models do not fit the empirical data in terms of traditional confirmatory factor analysis. Second, measurement invariance across age, which is necessary for a meaningful interpretation of age‐associated personality differences, is rarely accomplished. Finally, continuous moderator variables, such as age, are often artificially categorized. This categorization leads to bias when interpreting differences in personality across age. In this tutorial, we introduce methods to remedy these problems. We illustrate how Ant Colony Optimization can be used to sample indicators that meet prespecified demands such as model fit. Further, we use Local Structural Equation Modeling to resample and weight subjects to study differences in the measurement model across age as a continuous moderator variable. We also provide a detailed illustration for both tools with the Neuroticism scale of the openly available International Personality Item Pool – NEO inventory using data from the UK sample (N = 15 827). Combined, both tools can remedy persistent problems in research on personality and its development. In addition to a step‐by‐step illustration, we provide commented syntax for both tools. © 2019 European Association of Personality Psychology     

Using contextual effects to derive psychophysical scales

This paper presents a functional measurement analysis of Parducci’s range-frequency theory. The theory provides a basis for (1)finding context-invariant psychophysical scales, (2)establishing the validity of rating scales, and (3) explaining contextual effects in judgment. In an experimental illustration, Ss judged the magnitude of numerals in nine different distributions. All data were used to obtain the psychophysical function for numerals and also to test the model. The large contextual effects were consistent with the model. Quantitative tests of fit supported the equal-interval assumption of the category scale. The psychophysical function appeared nearly linear but with a significant negative acceleration. The data were shown to be qualitatively inconsistent with generalizations of Helson’s theory of adaptation level and Johnson’s correlation-regression theory. They supported Parducci’s range-frequency theory and illustrated how it could be used to factor out contextual effects from effects of stimulus magnitude. Extensions of the range-frequency approach are also discussed.     

Using IRT to separate measurement bias from true group differences on homogeneous and heterogeneous scales: an illustration with the MMPI

The authors present a didactic illustration of how item response theory (IRT) can be used to separate measurement bias from true group differences on homogeneous and heterogeneous scales. Several bias detection methods are illustrated with 12 unidimensional Minnesota Multiphasic Personality Inventory (MMPI) factor scales (Waller, 1999) and the 13 multidimensional MMPI validity and clinical scales. The article begins with a brief review of MMPI bias research and nontechnical reviews of the 2-parameter logistic model (2-PLM) and several IRT-based methods for bias detection. A goal of this article is to demonstrate that homogeneous and heterogeneous scales that are composed of biased items do not necessarily yield biased test scores. To that end, the authors perform differential item- and test-functioning analyses on the MMPI factor, validity, and clinical scales using data from 511 Blacks and 1,277 Whites from the California Youth Authority.     

Ordinary Least Squares Estimation of Parameters in Exploratory Factor Analysis With Ordinal Data

Exploratory factor analysis (EFA) is often conducted with ordinal data (e.g., items with 5-point responses) in the social and behavioral sciences. These ordinal variables are often treated as if they were continuous in practice. An alternative strategy is to assume that a normally distributed continuous variable underlies each ordinal variable. The EFA model is specified for these underlying continuous variables rather than the observed ordinal variables. Although these underlying continuous variables are not observed directly, their correlations can be estimated from the ordinal variables. These correlations are referred to as polychoric correlations. This article is concerned with ordinary least squares (OLS) estimation of parameters in EFA with polychoric correlations. Standard errors and confidence intervals for rotated factor loadings and factor correlations are presented. OLS estimates and the associated standard error estimates and confidence intervals are illustrated using personality trait ratings from 228 college students. Statistical properties of the proposed procedure are explored using a Monte Carlo study. The empirical illustration and the Monte Carlo study showed that (a) OLS estimation of EFA is feasible with large models, (b) point estimates of rotated factor loadings are unbiased, (c) point estimates of factor correlations are slightly negatively biased with small samples, and (d) standard error estimates and confidence intervals perform satisfactorily at moderately large samples.     

The Data Box and Within-Subject Analyses: A Comment on Nesselroade and Molenaar (2016)

Nesselroade and Molenaar suggest that it is the relationships between latent variables within subjects that are invariant across subjects and thus the appropriate unit of analysis. We disagree and take the view that between-factor correlations may differ systematically across subjects. Further, individual differences in these correlations may be an important source of information about each unique individual. Following from this premise, analyses of consistencies and differences between subjects of the within-subject pattern of interfactor correlations is a step toward an integrative science of behavior. We give several examples demonstrating how this approach has the potential to yield novel insights into personality functioning.     

Measurement‐Burst Designs for Social Health Research

Questions about variability and change in human behavior lie at the heart of much research in the behavioral sciences. This commentary examines the use of the measurement‐burst design ( Nesselroade, 1991 ) as an approach to study within‐person processes that transpire over very different temporal intervals. Consisting of repeated bursts of intensive (i.e., daily or momentary) assessments, the burst design can augment the type of information obtained from conventional daily diary and prospective longitudinal designs. We describe how the measurement‐burst approach can improve detection of long‐term intraindividual change, and how it can be used to study intraindividual variability and change in fine‐grained temporal relationships between daily experiences (e.g., hassles) and psychological states (e.g., mood). Some of the difficulties of implementing and analyzing data from measurement‐burst designs are discussed.     

Exploring Factor Model Parameters across Continuous Variables with Local Structural Equation Models

Using an empirical data set, we investigated variation in factor model parameters across a continuous moderator variable and demonstrated three modeling approaches: multiple-group mean and covariance structure (MGMCS) analyses, local structural equation modeling (LSEM), and moderated factor analysis (MFA). We focused on how to study variation in factor model parameters as a function of continuous variables such as age, socioeconomic status, ability levels, acculturation, and so forth. Specifically, we formalized the LSEM approach in detail as compared with previous work and investigated its statistical properties with an analytical derivation and a simulation study. We also provide code for the easy implementation of LSEM. The illustration of methods was based on cross-sectional cognitive ability data from individuals ranging in age from 4 to 23 years. Variations in factor loadings across age were examined with regard to the age differentiation hypothesis. LSEM and MFA converged with respect to the conclusions. When there was a broad age range within groups and varying relations between the indicator variables and the common factor across age, MGMCS produced distorted parameter estimates. We discuss the pros of LSEM compared with MFA and recommend using the two tools as complementary approaches for investigating moderation in factor model parameters.     

Testing neural network models of personality

Attempts to develop neural network models of personality have not generally used empirical data for training and validating the models. Two illustrations are provided which demonstrate the incorporation of empirical data into the modeling of behavioral responses to situations varying in closeness and hierarchical role relationships. An event-contingent recording procedure is utilized to obtain data from the same participant in multiple events for multiple situations. This data is then used in the training and validation of the neural networks. The first illustration models dominant and submissive behaviors in response to situations varying in social role status. The second illustration models agreeable and quarrelsome behaviors in response to situations varying in closeness and gender of the interaction partner. The predictions from both neural network models are consistent with previous research.     

Selecting the number of classes under latent class regression: a factor analytic analogue

Recently, the regression extension of latent class analysis (RLCA) model has received much attention in the field of medical research. The basic RLCA model summarizes shared features of measured multiple indicators as an underlying categorical variable and incorporates the covariate information in modeling both latent class membership and multiple indicators themselves. To reduce complexity and enhance interpretability, one usually fixes the number of classes in a given RLCA. Often, goodness of fit methods comparing various estimated models are used as a criterion to select the number of classes. In this paper, we propose a new method that is based on an analogous method used in factor analysis and does not require repeated fitting. Two ideas with application to many settings other than ours are synthesized in deriving the method: a connection between latent class models and factor analysis, and techniques of covariate marginalization and elimination. A Monte Carlo simulation study is presented to evaluate the behavior of the selection procedure and compare to alternative approaches. Data from a study of how measured visual impairments affect older persons’ functioning are used for illustration.This work was supported by National Institute on Aging (NIA) Program Project P01-AG-10184-03. The author wishes to thank Dr. Karen Bandeen-Roche for her stimulating comments and helpful discussions, and Drs. Gary Rubin and Sheila West for kindly making the Salisbury Eye Evaluation data available.