Statistical power of likelihood ratio and Wald tests in latent class models with covariates.

This paper discusses power and sample-size computation for likelihood ratio and Wald testing of the significance of covariate effects in latent class models. For both tests, asymptotic distributions can be used; that is, the test statistic can be assumed to follow a central Chi-square under the null hypothesis and a non-central Chi-square under the alternative hypothesis. Power or sample-size computation using these asymptotic distributions requires specification of the non-centrality parameter, which in practice is rarely known. We show how to calculate this non-centrality parameter using a large simulated data set from the model under the alternative hypothesis. A simulation study is conducted evaluating the adequacy of the proposed power analysis methods, determining the key study design factor affecting the power level, and comparing the performance of the likelihood ratio and Wald test. The proposed power analysis methods turn out to perform very well for a broad range of conditions. Moreover, apart from effect size and sample size, an important factor affecting the power is the class separation, implying that when class separation is low, rather large sample sizes are needed to achieve a reasonable power level.

Power Analysis for the Likelihood-Ratio Test in Latent Markov Models: Shortcutting the Bootstrap p-Value-Based Method.

The latent Markov (LM) model is a popular method for identifying distinct unobserved states and transitions between these states over time in longitudinally observed responses. The bootstrap likelihood-ratio (BLR) test yields the most rigorous test for determining the number of latent states, yet little is known about power analysis for this test. Power could be computed as the proportion of the bootstrap p values (PBP) for which the null hypothesis is rejected. This requires performing the full bootstrap procedure for a large number of samples generated from the model under the alternative hypothesis, which is computationally infeasible in most situations. This article presents a computationally feasible shortcut method for power computation for the BLR test. The shortcut method involves the following simple steps: (1) obtaining the parameters of the model under the null hypothesis, (2) constructing the empirical distributions of the likelihood ratio under the null and alternative hypotheses via Monte Carlo simulations, and (3) using these empirical distributions to compute the power. We evaluate the performance of the shortcut method by comparing it to the PBP method and, moreover, show how the shortcut method can be used for sample-size determination.

TRACING THE DEVELOPMENT OF TYPEWRITING SKILLS IN AN ADAPTIVE E-LEARNING ENVIRONMENT.

Typewriting studies which compare novice and expert typists have suggested that highly trained typing skills involve cognitive process with an inner and outer loop, which regulate keystrokes and words, respectively. The present study investigates these loops longitudinally, using multi-level modeling of 1,091,707 keystroke latencies from 62 children (M age=12.6 yr.) following an online typing course. Using finger movement repetition as indicator of the inner loop and words typed as indicator of the outer loop, practicing keystroke latencies resulted in different developmental curves for each loop. Moreover, based on plateaus in the developmental curves, the inner loop seemed to require less practice to develop than the outer loop.

Making Large-Scale Networks from fMRI Data.

Pairwise correlations are currently a popular way to estimate a large-scale network (> 1000 nodes) from functional magnetic resonance imaging data. However, this approach generally results in a poor representation of the true underlying network. The reason is that pairwise correlations cannot distinguish between direct and indirect connectivity. As a result, pairwise correlation networks can lead to fallacious conclusions; for example, one may conclude that a network is a small-world when it is not. In a simulation study and an application to resting-state fMRI data, we compare the performance of pairwise correlations in large-scale networks (2000 nodes) against three other methods that are designed to filter out indirect connections. Recovery methods are evaluated in four simulated network topologies (small world or not, scale-free or not) in scenarios where the number of observations is very small compared to the number of nodes. Simulations clearly show that pairwise correlation networks are fragmented into separate unconnected components with excessive connectedness within components. This often leads to erroneous estimates of network metrics, like small-world structures or low betweenness centrality, and produces too many low-degree nodes. We conclude that using partial correlations, informed by a sparseness penalty, results in more accurate networks and corresponding metrics than pairwise correlation networks. However, even with these methods, the presence of hubs in the generating network can be problematic if the number of observations is too small. Additionally, we show for resting-state fMRI that partial correlations are more robust than correlations to different parcellation sets and to different lengths of time-series.

Costs and benefits of automatization in category learning of ill-defined rules.

Learning ill-defined categories (such as the structure of Medin & Schaffer, 1978) involves multiple learning systems and different corresponding category representations, which are difficult to detect. Application of latent Markov analysis allows detection and investigation of such multiple latent category representations in a statistically robust way, isolating low performers and quantifying shifts between latent strategies. We reanalyzed data from three experiments presented in Johansen and Palmeri (2002), which comprised prolonged training of ill-defined categories, with the aim of studying the changing interactions between underlying learning systems. Our results broadly confirm the original conclusion that, in most participants, learning involved a shift from a rule-based to an exemplar-based strategy. Separate analyses of latent strategies revealed that (a) shifts from a rule-based to an exemplar-based strategy resulted in an initial decrease of speed and an increase of accuracy; (b) exemplar-based strategies followed a power law of learning, indicating automatization once an exemplar-based strategy was used; (c) rule-based strategies changed from using pure rules to rules-plus-exceptions, which appeared as a dual processes as indicated by the accuracy and response-time profiles. Results suggest an additional pathway of learning ill-defined categories, namely involving a shift from a simple rule to a complex rule after which this complex rule is automatized as an exemplar-based strategy.

Perceived causal relations between anxiety, posttraumatic stress and depression: extension to moderation, mediation, and network analysis.

BACKGROUND: Previous research demonstrates that posttraumatic memory reexperiencing, depression, anxiety, and guilt-shame are frequently co-occurring problems that may be causally related. OBJECTIVES: The present study utilized Perceived Causal Relations (PCR) scaling in order to assess participants' own attributions concerning whether and to what degree these co-occurring problems may be causally interrelated. METHODS: 288 young adults rated the frequency and respective PCR scores associating their symptoms of posttraumatic reexperiencing, depression, anxiety, and guilt-shame. RESULTS: PCR scores were found to moderate associations between the frequency of posttraumatic memory reexperiencing, depression, anxiety, and guilt-shame. Network analyses showed that the number of feedback loops between PCR scores was positively associated with symptom frequencies. CONCLUSION: Results tentatively support the interpretation of PCR scores as moderators of the association between different psychological problems, and lend support to the hypothesis that increased symptom frequencies are observed in the presence of an increased number of causal feedback loops between symptoms. Additionally, a perceived causal role for the reexperiencing of traumatic memories in exacerbating emotional disturbance was identified.

Distinct discrimination learning strategies and their relation with spatial memory and attentional control in 4- to 14-year-olds.

Behavioral, psychophysiological, and neuropsychological studies have revealed large developmental differences in various learning paradigms where learning from positive and negative feedback is essential. The differences are possibly due to the use of distinct strategies that may be related to spatial working memory and attentional control. In this study, strategies in performing a discrimination learning task were distinguished in a cross-sectional sample of 302 children from 4 to 14 years of age. The trial-by-trial accuracy data were analyzed with mathematical learning models. The best-fitting model revealed three learning strategies: hypothesis testing, slow abrupt learning, and nonlearning. The proportion of hypothesis-testing children increased with age. Nonlearners were present only in the youngest age group. Feature preferences for the irrelevant dimension had a detrimental effect on performance in the youngest age group. The executive functions spatial working memory and attentional control significantly predicted posterior learning strategy probabilities after controlling for age.

The small world of psychopathology.

BACKGROUND: Mental disorders are highly comorbid: people having one disorder are likely to have another as well. We explain empirical comorbidity patterns based on a network model of psychiatric symptoms, derived from an analysis of symptom overlap in the Diagnostic and Statistical Manual of Mental Disorders-IV (DSM-IV). PRINCIPAL FINDINGS: We show that a) half of the symptoms in the DSM-IV network are connected, b) the architecture of these connections conforms to a small world structure, featuring a high degree of clustering but a short average path length, and c) distances between disorders in this structure predict empirical comorbidity rates. Network simulations of Major Depressive Episode and Generalized Anxiety Disorder show that the model faithfully reproduces empirical population statistics for these disorders. CONCLUSIONS: In the network model, mental disorders are inherently complex. This explains the limited successes of genetic, neuroscientific, and etiological approaches to unravel their causes. We outline a psychosystems approach to investigate the structure and dynamics of mental disorders.

Transdiagnostic Networks: Commentary on Nolen-Hoeksema and Watkins (2011).

Nolen-Hoeksema and Watkins (2011, this issue) propose a useful model for thinking about transdiagnostic processes involved in mental disorders. Here, we argue that their model is naturally compatible with a network account of mental disorders, in which disorders are viewed as sets of mutually reinforcing symptoms. We show that network models are typically transdiagnostic in nature, because different disorders often share symptoms. We illustrate this by constructing a network for generalized anxiety and major depression. In addition, we show that even a simple network structure naturally accounts for the phenomena of multifinality and divergent trajectories that Nolen-Hoeksema and Watkins identify as crucial in thinking about transdiagnostic phenomena.

Parameter identification in multinomial processing tree models.

Multinomial processing tree models form a popular class of statistical models for categorical data that have applications in various areas of psychological research. As in all statistical models, establishing which parameters are identified is necessary for model inference and selection on the basis of the likelihood function, and for the interpretation of the results. The required calculations to establish global identification can become intractable in complex models. We show how to establish local identification in multinomial processing tree models, based on formal methods independently proposed by Catchpole and Morgan (1997) and by Bekker, Merckens, and Wansbeek (1994). This approach is illustrated with multinomial processing tree models for the source-monitoring paradigm in memory research.

Multiple learning modes in the development of performance on a rule-based category-learning task.

Behavioral and neuropsychological data suggest that multiple systems are involved in category-learning. In this paper, the existence and the development of multiple modes of learning of a rule-based category structure was examined, and features of different learning processes were identified. Data were obtained in a cross-sectional study by Raijmakers et al. [Raijmakers, M. E. J., Dolan, C. V., & Molenaar, P. C. M. (2001). Finite mixture distribution models of simple discrimination learning. Memory and Cognition, 29, 659-677], in which subjects aged 4-20 years carried out a rule-based category-learning task. Learning models were employed to investigate the development of the learning processes in the sample. The results support the hypothesis of two distinct learning modes, rather than a single general mode of learning with a continuum of appearances. One mode represents sudden rational learning by means of hypothesis testing. In the second, slow learning mode, learning also occurs suddenly as opposed to incrementally. The probability of rational learning increases with age, and seems to be related to dimension preference in the younger age groups. However, the finding of distinct learning modes does not necessarily imply that distinct learning systems are involved. Implications for the interpretation and clinical use of tasks with a category-learning component, such as the Wisconsin Card Sorting Test (WCST [Heaton, R. K., Chelune, G. J., Talley, J. L., Kay, G. G., & Curtis, G. (Eds.). (1993). Wisconsin card sorting test manual: Revised and expanded. Odessa, FL: Psychological Assessment Resources]), are discussed.

Discrete Latent Markov Models for Normally Distributed Response Data.

Van de Pol and Langeheine (1990) presented a general framework for Markov modeling of repeatedly measured discrete data. We discuss analogical single indicator models for normally distributed responses. In contrast to discrete models, which have been studied extensively, analogical continuous response models have hardly been considered. These models are formulated as highly constrained multinormal finite mixture models (McLachlan & Peel, 2000). The assumption of conditional independence, which is often postulated in the discrete models, may be relaxed in the normal-based models. In these models, the observed correlation between two variables may thus be due to the presence of two or more latent classes and the presence of within-class dependence. The latter may be subjected to structural equation modeling. In addition to presenting various normal-based Markov models, we demonstrate how these models, formulated as multinormal finite mixtures, may be fitted using the freely available program Mx (Neale, Boker, Xie, & Maes, 2002). To illustrate the application of some of the models, we report the analysis of data relating to the understanding of the conservation of continuous quantity (i.e., a Piagetian construct).