A latent growth‐curve approach to difficult temperament

A purported hallmark of temperament characteristics is that they appear very early in the course of development and are persistent across time and situation. There is, however, a small, but growing cadre of research findings that question this traditional view. It may be that temperament characteristics are not necessarily established during the first few months of development or are not stable over time. A secondary analysis of the New York Longitudinal Study (NYLS) temperament data was conducted to investigate the hypothesis that temperament has a complex developmental course over the first five years of development. A latent growth curve analysis of difficult temperament suggests that temperament development follows a non‐linear trajectory. This finding, in concert with related findings, suggests the need for a broader discussion of the possible developmental processes that underlie these patterns. Copyright © 2007 John Wiley & Sons, Ltd.     

Developmental patterns in body esteem from late childhood to young adulthood: A growth curve analysis

This study examines the long-term development of different domains of body esteem (BE), the most salient domain of adolescents' global self-esteem. The 11-year longitudinal study of Swedish youths, covering ages 10–21, showed that BE undergoes significant change from late childhood to young adulthood, with growth curve models revealing different developmental paths between domains and across gender. For girls, general appearance esteem and weight esteem decreased in the early adolescent phase and then stabilized. For boys, similar patterns were evident, but weight esteem was subject to change also in late adolescence. The third BE domain, appearance-evaluations ascribed to others, displayed a distinct developmental trajectory. This was the only domain where no gender differences were noted in terms of mean levels. It was also the only domain that demonstrated positive increases over time. Findings from the present long-term study contribute to a more coherent picture of the development of BE from late childhood and into young adulthood.     

Logistic growth curve analysis in associative learning data

We propose an alternative statistical method, logistic growth curve analysis, for the analysis of associative learning data with two or more comparison groups. Logistic growth curve analysis is more sensitive and easier to interpret than previously published methods such as χ² or ANOVA, which require the data to be collapsed into individual total scores or proportion of responses over time. Additionally, this type of analysis better fits the typical graphical representation of associative learning data. An analysis is presented where associative learning data from honeybees are analyzed using the three techniques, and the accessibility and power of the logistic growth curve analysis is highlighted. Accepted after revision: 14 November 2000 Electronic Publication     

Self-face advantage over familiar and unfamiliar faces: A three-level meta-analytic approach

Despite the increasing number of researchers interested in self-face, so far, no study has summarized the behavioral findings that contribute to the debate on self-face advantage. Most studies have focused on neural correlates of the self, although functional uniqueness can also be considered an important criterion for determining whether a stimulus is unique. The present meta-analysis systematically compared reaction time (RT) responses for self-face with other face identities across 54 studies. Different moderator factors were tested: familiarity, identity, head angle, laterality, and culture. We used a three-level meta-analytic approach, which is the best approach to account for the dependency of effect sizes. Results showed a significant (Hedges’s g_av = ?0.298) effect size, indicating faster RT for self-face than for other faces in general. Except for culture, none of the moderators employed significantly impacted on the main effect. Regarding culture, results showed that participants from Western cultures tend to respond faster to their own face than to other people’s faces, while for participants from Eastern cultures, the effect was not significant. In summary, our results indicate that the self-face benefits from an advantage in terms of reaction time and may be considered a unique stimulus. Implications and limitations of the results are discussed.     

Statistical power analysis for growth curve models using SAS

Power analysis is critical in research designs. This study discusses a simulation-based approach utilizing the likelihood ratio test to estimate the power of growth curve analysis. The power estimation is implemented through a set of SAS macros. The application of the SAS macros is demonstrated through several examples, including missing data and nonlinear growth trajectory situations. The results of the examples indicate that the power of growth curve analysis increases with the increase of sample sizes, effect sizes, and numbers of measurement occasions. In addition, missing data can reduce power. The SAS macros can be modified to accommodate more complex power analysis for both linear and nonlinear growth curve models.     

Statistical power of latent growth curve models to detect quadratic growth

Latent curve models (LCMs) have been used extensively to analyze longitudinal data. However, little is known about the power of LCMs to detect nonlinear trends when they are present in the data. For this study, we utilized simulated data to investigate the power of LCMs to detect the mean of the quadratic slope, Type I error rates, and rates of nonconvergence during the estimation of quadratic LCMs. Five factors were examined: the number of time points, growth magnitude, interindividual variability, sample size, and the R ²s of the measured variables. The results showed that the empirical Type I error rates were close to the nominal value of 5 %. The empirical power to detect the mean of the quadratic slope was affected by the simulation factors. Finally, a substantial proportion of samples failed to converge under conditions of no to small variation in the quadratic factor, small sample sizes, and small R ² of the repeated measures. In general, we recommended that quadratic LCMs be based on samples of (a) at least 250 but ideally 400, when four measurement points are available; (b) at least 100 but ideally 150, when six measurement points are available; (c) at least 50 but ideally 100, when ten measurement points are available.     

Initial goals,goal trajectories,and serial argument resolvability: A growth curve analysis

This study examines dyadic patterns of goal pursuit during a serial argument interaction and their associations with perceived argument resolvability. The authors utilize a growth curve framework to highlight how both initial importance and trajectories (i.e., over‐time increases/decreases) of goal importance predicted perceived resolvability. Seventy‐six heterosexual couples discussed a current serial argument and reported their goals at 1‐min increments, using a video‐assisted recall method. Both initial importance and increases in actors' partner‐focused goals were positively associated with perceived resolvability, and increases in a partners' self‐focused goal importance across the course of the interaction were negatively associated with actors' postinteraction resolvability perceptions. Results suggest that partners should attend to both initial goals and trajectories of goal pursuit during argumentative interactions.     

A bayesian approach to confirmatory factor analysis

Confirmatory factor analysis is considered from a Bayesian viewpoint, in which prior information on parameter is incorporated in the analysis. An iterative algorithm is developed to obtain the Bayes estimates. A numerical example based on longitudinal data is presented. A simulation study is designed to compare the Bayesian approach with the maximum likelihood method.Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong.     

A general approach to nonlinear factor analysis

The method presented attempts to allow for nonlinear, possibly nonmonotonic relations between manifest and latent variates. An attempt is made to provide a workable criterion for choosing between alternative models on the basis of observable data as well as for constructing the appropriate function. An idealized numerical example is given.The author is indebted to Mr. E. J. Burr of the Department of Mathematics, University of New England, and to Dr. J. A. Keats of the University of Queensland, for their advice and criticism.     

A general approach to causal mediation analysis

Traditionally in the social sciences, causal mediation analysis has been formulated, understood, and implemented within the framework of linear structural equation models. We argue and demonstrate that this is problematic for 3 reasons: the lack of a general definition of causal mediation effects independent of a particular statistical model, the inability to specify the key identification assumption, and the difficulty of extending the framework to nonlinear models. In this article, we propose an alternative approach that overcomes these limitations. Our approach is general because it offers the definition, identification, estimation, and sensitivity analysis of causal mediation effects without reference to any specific statistical model. Further, our approach explicitly links these 4 elements closely together within a single framework. As a result, the proposed framework can accommodate linear and nonlinear relationships, parametric and nonparametric models, continuous and discrete mediators, and various types of outcome variables. The general definition and identification result also allow us to develop sensitivity analysis in the context of commonly used models, which enables applied researchers to formally assess the robustness of their empirical conclusions to violations of the key assumption. We illustrate our approach by applying it to the Job Search Intervention Study. We also offer easy-to-use software that implements all our proposed methods.     

Latent growth curve analysis with dichotomous items: Comparing four approaches

A Monte Carlo study was used to compare four approaches to growth curve analysis of subjects assessed repeatedly with the same set of dichotomous items: A two‐step procedure first estimating latent trait measures using MULTILOG and then using a hierarchical linear model to examine the changing trajectories with the estimated abilities as the outcome variable; a structural equation model using modified weighted least squares (WLSMV) estimation; and two approaches in the framework of multilevel item response models, including a hierarchical generalized linear model using Laplace estimation, and Bayesian analysis using Markov chain Monte Carlo (MCMC). These four methods have similar power in detecting the average linear slope across time. MCMC and Laplace estimates perform relatively better on the bias of the average linear slope and corresponding standard error, as well as the item location parameters. For the variance of the random intercept, and the covariance between the random intercept and slope, all estimates are biased in most conditions. For the random slope variance, only Laplace estimates are unbiased when there are eight time points.     

A multivariate reduced-rank growth curve model with unbalanced data

A multivariate reduced-rank growth curve model is proposed that extends the univariate reducedrank growth curve model to the multivariate case, in which several response variables are measured over multiple time points. The proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way than the traditional growth curve model. In addition, the method is more flexible than the traditional growth curve model. For example, response variables do not have to be measured at the same time points, nor the same number of time points. It is also possible to apply various kinds of basis function matrices with different ranks across response variables. It is not necessary to specify an entire set of basis functions in advance. Examples are given for illustration.The work reported in this paper was supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the second author. We thank Jennifer Stephan for her helpful comments on an earlier version of this paper. We also thank Patrick Curran and Terry Duncan for kindly letting us use the NLSY and substance use data, respectively. The substance use data were provided by Grant DA09548 from the National Institute on Drug Abuse.     

A neural network approach to movement pattern analysis

Movements are time-dependent processes and so can be modelled by time-series of coordinates: E.g., each articulation has geometric coordinates; the set of the coordinates of the relevant articulations build a high-dimensional configuration. These configurations--or "patterns"--give reason for analysing movements by means of neural networks: The Kohonen Feature Map (KFM) is a special type of neural network, which (after having been coined by training with appropriate pattern samples) is able to recognize single patterns as members of pattern clusters. This way, for example, the particular configurations of a given movement can be identified as belonging to respective configuration clusters, where the sequence of clusters to which the time-depending configurations belong, characterizes the process as a 2-dimensional trajectory. The advantages of this method are that: the high dimensionality of the original processes is reduced to two dimensional trajectories, the clusters are automatically determined by the network, and all data for further analyses can automatically be transferred into a data base. Thus, the processes can either be visualized and analysed by an expert or again processed by further automatic analysing tools, as has been done with similarity matrices. The disadvantage is that a KFM-training needs a huge amount of information, which normally is not available from experiments. However, the Dynamically Controlled Network DyCoN (a special type of KFM) makes it possible to reduce the amount of original training data substantially--e.g., by adding stochastically generated ones. Currently, DyCoN is used in several projects in order to generally support analyses of processes in sport. It should be emphasized that the presented approach is not meant to improve the understanding or to develop models of human movement but to give a survey of the advantages and methodological aspects of net-based movement analysis.     

A similarity-based smoothing approach to nondimensional item analysis

The probability that an examinee chooses a particular option within an item is estimated by averaging over the responses to that item of examinees with similar response patterns for the whole test. The approach does not presume any latent variable structure or any dimensionality. But simulated and actual data analyses are presented to show that when the responses are determined by a latent ability variable, this similarity-based smoothing procedure can reveal the dimensionality of ability very satisfactorily.The author wishes to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada through grant A320, and to thank Educational Testing Service for making the data on the Advanced Placement Chemistry Exam available.     

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.