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Murphy (2021) argues that the field of Industrial-Organizational (I/O) Psychology needs to pay more attention to descriptive statistics ('Table 1'; e.g., M, SD, reliability, correlations) when reporting and interpreting results. We agree that authors need to present a clear and transparent description of their data and that descriptive statistics and plots can be helpful in making sense of one's data and analyses (Tay et al., 2016). Many journals already require this. Although this information can be presented in the manuscript, more details can be placed in online supplements where there are fewer space limitations (e.g., detailed presentation and discussion of descriptive statistics, missing data and outliers, plots and diagrams, conceptual issues, and computer syntax). However, we strongly disagree with the claim that 'increasing complexity and diversity of data-analytic methods in organizational research has created several problems in our field' (p. 2). This claim suffers from two important oversights: (1) it neglects the crucial role of methodological fit, or the notion that theory, methods, and analyses need to be aligned, and (2) it neglects the fact that in I/O research, most constructs are not directly observable but need to be inferred indirectly though latent variable models. We expand on both issues, using examples to illustrate that the complexity and diversity of data-analytic methods is not a threat but a blessing for I/O research (and beyond). Finally, we conclude by highlighting the need for substantive-methodological synergies to solve some of the issues raised by Murphy (2021).

This article compares a general cross-lagged model (GCLM) to other panel data methods based on their coherence with a causal logic and pragmatic concerns regarding modeled dynamics and hypothesis testing. We examine three “static” models that do not incorporate temporal dynamics: random- and fixed-effects models that estimate contemporaneous relationships; and latent curve models. We then describe “dynamic” models that incorporate temporal dynamics in the form of lagged effects: cross-lagged models estimated in a structural equation model (SEM) or multilevel model (MLM) framework; Arellano-Bond dynamic panel data methods; and autoregressive latent trajectory models. We describe the implications of overlooking temporal dynamics in static models and show how even popular cross-lagged models fail to control for stable factors over time. We also show that Arellano-Bond and autoregressive latent trajectory models have various shortcomings. By contrasting these approaches, we clarify the benefits and drawbacks of common methods for modeling panel data, including the GCLM approach we propose. We conclude with a discussion of issues regarding causal inference, including difficulties in separating different types of time-invariant and time-varying effects over time. Australian Research Council https://doi.org/10.13039/501100000923

his is the first paper in a series of two that synthesizes, compares, and extends methods for causal inference with longitudinal panel data in a structural equation modeling (SEM) framework. Starting with a cross-lagged approach, this paper builds a general cross-lagged panel model (GCLM) with parameters to account for stable factors while increasing the range of dynamic processes that can be modeled. We illustrate the GCLM by examining the relationship between national income and subjective well-being (SWB), showing how to examine hypotheses about short-run (via Granger-Sims tests) versus long-run effects (via impulse responses). When controlling for stable factors, we find no short-run or long-run effects among these variables, showing national SWB to be relatively stable, whereas income is less so. Our second paper addresses the differences between the GCLM and other methods. Online Supplementary Materials offer an Excel file automating GCLM input for Mplus (with an example also for Lavaan in R) and analyses using additional data sets and all program input/output. We also offer an introductory GCLM presentation at https://youtu.be/tHnnaRNPbXs. We conclude with a discussion of issues surrounding causal inference. All authors: Michael J. Zyphur, Paul D. Allison, Louis Tay, Manuel C. Voelkle, Kristopher J. Preacher, Zhen Zhang, Ellen L. Hamaker, Ali Shamsollahi, Dean C. Pierides, Peter Koval, Ed Diener

With the growing popularity of intensive longitudinal research, the modeling techniques and software options for such data are also expanding rapidly. Here we use dynamic multilevel modeling, as it is incorporated in the new dynamic structural equation modeling (DSEM) toolbox in Mplus, to analyze the affective data from the COGITO study. These data consist of two samples of over 100 individuals each who were measured for about 100 days. We use composite scores of positive and negative affect and apply a multilevel vector autoregressive model to allow for individual differences in means, autoregressions, and cross-lagged effects. Then we extend the model to include random residual variances and covariance, and finally we investigate whether prior depression affects later depression scores through the random effects of the daily diary measures. We end with discussing several urgent—but mostly unresolved—issues in the area of dynamic multilevel modeling.

In many disciplines researchers use longitudinal panel data to investigate the potentially causal relationship between 2 variables. However, the conventions and concerns vary widely across disciplines. Here we focus on 2 concerns, that is: (a) the concern about random effects versus fixed effects, which is central in the (micro)econometrics/sociology literature; and (b) the concern about grand mean versus group (or person) mean centering, which is central in the multilevel literature associated with disciplines like psychology and educational sciences. We show that these 2 concerns are actually addressing the same underlying issue. We discuss diverse modeling methods based on either multilevel regression modeling with the data in long format, or structural equation modeling with the data in wide format, and compare these approaches with simulated data. We extend the multilevel model with random slopes and discuss the consequences of this. Subsequently, we provide guidelines on how to choose between the diverse modeling options. We illustrate the use of these guidelines with an empirical example based on intensive longitudinal data, in which we consider both a time-varying and a time-invariant covariate. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Only for ergodic processes will inferences based on group-level data generalize to individual experience or behavior. Because human social and psychological processes typically have an individually variable and time-varying nature, they are unlikely to be ergodic. In this paper, six studies with a repeated-measure design were used for symmetric comparisons of interindividual and intraindividual variation. Our results delineate the potential scope and impact of nonergodic data in human subjects research. Analyses across six samples (with 87-94 participants and an equal number of assessments per participant) showed some degree of agreement in central tendency estimates (mean) between groups and individuals across constructs and data collection paradigms. However, the variance around the expected value was two to four times larger within individuals than within groups. This suggests that literatures in social and medical sciences may overestimate the accuracy of aggregated statistical estimates. This observation could have serious consequences for how we understand the consistency between group and individual correlations, and the generalizability of conclusions between domains. Researchers should explicitly test for equivalence of processes at the individual and group level across the social and medical sciences.

An increasing number of researchers in psychology are collecting intensive longitudinal data in order to study psychological processes on an intraindividual level. An increasingly popular way to analyze these data is autoregressive time series modeling; either by modeling the repeated measures for a single individual using classic n = 1 autoregressive models, or by using multilevel extensions of these models, with the dynamics for each individual modeled at Level 1 and interindividual differences in these dynamics modeled at Level 2. However, while it is widely accepted in psychology that psychological measurements usually contain a certain amount of measurement error, the issue of measurement error is largely neglected in applied psychological (autoregressive) time series modeling: The regular autoregressive model incorporates innovations, or "dynamic errors," but not measurement error. In this article we discuss the concepts of reliability and measurement error in the context of dynamic (VAR(1)) models, and the consequences of disregarding measurement error variance in the data. For this purpose, we present a preliminary model that accounts for measurement error for constructs that are measured with a single indicator. We further discuss how this model could be used to investigate the between-person reliability of the measurements, as well as the (person-specific) within-person reliabilities and any individual differences in these reliabilities. We illustrate the consequences of assuming perfect reliability, the preliminary model, and reliabilities, using an empirical application in which we relate women's general positive affect to their positive affect concerning their romantic relationship. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Time series analysis is a technique that can be used to analyze the data from a single subject and has great potential to investigate clinically relevant processes like affect regulation. This article uses time series models to investigate the assumed dysregulation of affect that is associated with bipolar disorder. By formulating a number of alternative models that capture different kinds of theoretically predicted dysregulation, and by comparing these in both bipolar patients and controls, we aim to illustrate the heuristic potential this method of analysis has for clinical psychology. We argue that, not only can time series analysis elucidate specific maladaptive dynamics associated with psychopathology, it may also be clinically applied in symptom monitoring and the evaluation of therapeutic interventions.

Intra-individual variability over a short period of time may contain important information about how individuals differ from each other. In this article we begin by discussing diverse indicators for quantifying intra-individual variability and indicate their advantages and disadvantages. Then we propose an alternative method that models inter-individual differences in intra-individual variability by separately considering both the amplitude of fluctuations and temporal dependency in the data. In the proposed model, temporal dependency and amplitude of fluctuations are both included as random effects. Parameter estimation is done with a multiple-step approach using maximum likelihood, or with a recommended 1-step approach using a Bayesian method. The similarities and differences between the proposed method and some existing methods are discussed and investigated using diary study data from older adults. The results from empirical data analysis revealed that temporal dependency and amplitude of fluctuations have different predictability of health outcomes and thus should be modeled and considered separately.

Many psychological processes are characterized by recurrent shifts between distinct regimes or states. Examples that are considered in this paper are the switches between different states associated with premenstrual syndrome, hourly fluctuations in affect during a major depressive episode, and shifts between a "hot hand" and a "cold hand" in a top athlete. We model these processes with the regime switching state-space model proposed by Kim ("J. Econom." 60:1-22, 1994), which results in both maximum likelihood estimates for the model parameters and estimates of the latent variables and the discrete states of the process. However, the current algorithm cannot handle missing data, which limits its applicability to psychological data. Moreover, the performance of standard errors for the purpose of making inferences about the parameter estimates is yet unknown. In this paper we modify Kim's algorithm so it can handle missing data and we perform a simulation study to investigate its performance in (relatively) short time series in cases of different kinds of missing data and in case of complete data. Finally, we apply the regime switching state-space model to the three empirical data sets described above.

Gottman and colleagues proposed using a dynamical systems model to study dyadic interaction in marriage. In this model, each spouse's affect in each 6-s window is described as a function of an uninfluenced linear steady state and a nonlinear influence function of the partner's affect in the previous window. Recently, an alternative parameter estimation procedure for the equations of marriage was introduced, which is based on threshold autoregressive models. We apply this estimation procedure to data from a study of couples (N = 124) and newlyweds (N = 130) to compare different forms of spousal influence using the Bayesian information criterion. Although results show some statistically significant evidence for influence, this is only slightly greater than what would be expected by random association. One model of influence does not fit all couples. This suggests that for many people initial state and emotional inertia dictate the outcome of the conflict discussion far more than the moment-to-moment affect of the spouse. This latter finding is in conflict with most models of couples' interaction, which suggest that the outcome of conflict discussions are determined by the nature of the couples' mutual influence processes.

State-space modeling techniques have been compared to structural equation modeling (SEM) techniques in various contexts but their unique strengths have often been overshadowed by their similarities to SEM. In this article, we provide a comprehensive discussion of these 2 approaches' similarities and differences through analytic comparisons and numerical simulations, with a focus on their use in representing intraindividual dynamics and interindividual differences. To demonstrate the respective strengths and weaknesses of the 2 approaches in representing these 2 aspects, we simulated data under (a) a cross-sectional common factor model, (b) a latent difference score model with random effects in intercept and slope, and (c) a bivariate dynamic factor analysis model with auto- and cross-regression parameters. Possible ways in which SEM and state-space modeling can be utilized as complementary tools in representing human developmental and other related processes are discussed.

Threshold autoregressive models can be used to study processes that are characterized by recurrent switches between two or more regimes, where switching is triggered by a manifest threshold variable. In this paper the performance of diverse information criteria for selecting the number of regimes in small to moderate sample sizes (i.e., n = 50 , 100 , 200 ) is investigated. In addition it is investigated whether these information criteria can be used to determine whether the residual variances are identical across the regimes. It is concluded that for small sample sizes AIC u should be preferred, while for larger sample sizes either BIC or AIC c p should be considered: The latter is the only information criterion that includes a penalty for the unknown threshold parameters.

Over the last few decades, researchers have become increasingly aware of the need to consider intraindividual variability in the form of cyclic processes. In this paper, we review two contemporary cyclic state-space models: Young and colleagues' dynamic harmonic regression model and Harvey and colleagues' stochastic cycle model. We further derive the analytic equivalence between the two models, discuss their unique strengths and propose multiple-subject extensions. Using data from a study on human postural dynamics and a daily affect study, we demonstrate the use of these models to represent within-person non-stationarities in cyclic dynamics and interindividual differences therein. The use of diagnostic tools for evaluating model fit is also illustrated.

Outliers are typically regarded as data anomalies that should be discarded. However, dynamic or "innovative" outliers can be appropriately utilized to capture unusual but substantively meaningful shifts in a system's dynamics. We extend De Jong and Penzer's 1998 approach for representing outliers in single-subject state-space models to a group-based framework. The group-based model enables model predictions concerning the group as a whole while individualized change points are incorporated to capture discrete shifts in each individual's trajectory. An illustrative example using cognitive performance data from N = 38 older adults over 60 days is presented. Results indicated that a subset of older adults showed sudden shifts in learning dynamics in several forms, including sudden jumps in level, slope, and linkage between perceived control and actual performance level. The broader implications of incorporating innovative outliers into studies of intraindividual change are discussed.

Considering a dyad as a dynamic system whose current state depends on its past state has allowed researchers to investigate whether and how partners influence each other. Some researchers have also focused on how differences between dyads in their interaction patterns are related to other differences between them. A promising approach in this area is the model that was proposed by Gottman and Murray, which is based on nonlinear coupled difference equations. In this paper, it is shown that their model is a special case of the threshold autoregressive (TAR) model. As a consequence, we can make use of existing knowledge about TAR models with respect to parameter estimation, model alternatives and model selection. We propose a new estimation procedure and perform a simulation study to compare it to the estimation procedure developed by Gottman and Murray. In addition, we include an empirical example based on interaction data of three dyads.

Four methods for estimating a dynamic factor model, the direct autoregressive factor score (DAFS) model, are evaluated and compared. The first method estimates the DAFS model using a Kalman filter algorithm based on its state space model representation. The second one employs the maximum likelihood estimation method based on the construction of a block-Toeplitz covariance matrix in the structural equation modeling framework. The third method is built in the Bayesian framework and implemented using Gibbs sampling. The fourth is the least squares method, which also employs the block-Toeplitz matrix. All 4 methods are implemented in currently available software. The simulation study shows that all 4 methods reach appropriate parameter estimates with comparable precision. Differences among the 4 estimation methods and related software are discussed.

(2007). Commentary: How to Inspect Fruit. Measurement: Interdisciplinary Research and Perspectives: Vol. 5, No. 4, pp. 250-253.

It has been acknowledged that both trait and state contribute to psychological measurements. However, existing structural equation models for disentangling these sources of variability are based on assumptions that are not tenable in the light of empirical results. A new model is presented, termed the integrated trait–state (ITS) model, which both decomposes state and trait variance and allows one to test the assumptions that underly existing approaches. This is illustrated with an empirical example. The relationship between the ITS model and other analytic approaches as well as conceptual models of traits and states are discussed.

The cross-lagged panel model (CLPM) is believed by many to overcome the problems associated with the use of cross-lagged correlations as a way to study causal influences in longitudinal panel data. The current article, however, shows that if stability of constructs is to some extent of a trait-like, time-invariant nature, the autoregressive relationships of the CLPM fail to adequately account for this. As a result, the lagged parameters that are obtained with the CLPM do not represent the actual within-person relationships over time, and this may lead to erroneous conclusions regarding the presence, predominance, and sign of causal influences. In this article we present an alternative model that separates the within-person process from stable between-person differences through the inclusion of random intercepts, and we discuss how this model is related to existing structural equation models that include cross-lagged relationships. We derive the analytical relationship between the cross-lagged parameters from the CLPM and the alternative model, and use simulations to demonstrate the spurious results that may arise when using the CLPM to analyze data that include stable, trait-like individual differences. We also present a modeling strategy to avoid this pitfall and illustrate this using an empirical data set. The implications for both existing and future cross-lagged panel research are discussed.

Results obtained with interindividual techniques in a representative sample of a population are not necessarily generalizable to the individual members of this population. In this article the specific condition is presented that must be satisfied to generalize from the interindividual level to the intraindividual level. A way to investigate whether this condition is satisfied is by means of multivariate time series analysis. More generally, time series analysis can be used to investigate psychological processes situated within individuals. In this article we consider a well established class of multivariate stationary time series models that may be used to study the intraindividual covariance structure. We demonstrate the application of some of these models with an empirical example consisting of state measurements of behavior associated with the Five Factor Model of Personality. We illustrate how one can investigate whether individuals are similar with respect to their intraindividual structure of variation, and whether this structure is similar to the structure of interindividual variation.

Longitudinal structural equation modeling has generally addressed the time-dependent covariance structure of a relatively small number of repeated measures, T, observed in a relatively large representative sample, N. In contrast, the literature on autoregressive moving average modeling is usually directed at a single realization comprising many observations, that is, N = 1, and T > 50. This article deals with autoregressive moving average-based structural equation modeling of time series data, in the situation that N is small, T is intermediate, and T > N. The aims of this article are to (a) give a brief overview of the development of alternative formulations of the likelihood function to obtain estimates of autoregressive moving average parameters, in particular the formulation that lies at the basis of Melard's algorithm; (b) show the equivalence between the likelihood function to obtain estimates for these parameters, and the raw data likelihood method that can be used in structural equation modeling p...

The aim of this article is to (a) reexamine the nature of structural equation modeling (SEM) estimates of autoregressive moving average (ARMA) parameters; (b) replicate S. Van Buuren's simulation experiment in light of P. C. M. Molenaar's comment; and (c) examine the behavior of the log-likelihood ratio test. It is concluded that estimates of ARMA parameters obtained with SEM software are identical to those obtained by univariate stochastic model preliminary estimation, and are not true maximum likelihood (ML) estimates. Still, these estimates, which may be viewed as moment estimates, have the same asymptotic properties as ML estimates for pure autoregressive (AR) processes. For pure moving average (MA) processes, they are biased and less efficient. The estimates from SEM software for mixed processes seem to have the same asymptotic properties as ML estimates. Furthermore, the log-likelihood ratio is reliable for pure AR processes, but this is not the case for pure MA processes. For mixed processes, the behavior of the log-likelihood ratio varies, and in this case these statistics should be handled with caution.

Many psychological processes are characterized by recurrent shifts between different states. To model these processes at the level of the individual, regime-switching models may prove useful. In this chapter we discuss two of these models: the threshold autoregressive model and the Markov switching autoregressive model. We discuss their main features, and propose estimation methods that can handle missing data. We apply these models to daily affect measurements of an individual diagnosed with rapid cycling bipolar disorder.

A non-clinical group high on heterogeneous medically unexplained symptoms (MUS; n=97) was compared with healthy controls (n=66) on the within-subject relationships between physiological measures using multilevel path analysis. Momentary experienced somatic complaints, mood (tension and depression), cardiac autonomic activity (inter-beat intervals, pre-ejection period (PEP), and respiratory sinus arrhythmia (RSA)) and respiration (rate and partial pressure of CO(2) at the end of a normal expiration) were monitored for 24 h using electronic diary and ambulatory devices. Relationships between measures were controlled for diurnal variation and individual means. Only subtle group differences were found in the diurnal rhythm and in the within-subject relationships between physiological measures. For participants high on MUS, within-subject changes in bodily symptoms were related to changes in mood, but only marginally to the physiological measures. Results of the current path analysis confirm the subordinate role of cardiac autonomic and respiratory parameters in MUS.

Curran and Bollen combined two models for longitudinal panel data: the latent growth curve model and the autoregressive model. In their model, the autoregressive relationships are modeled between the observed variables. This is a different model than a latent growth curve model with autoregressive relationships between the disturbances. However, when the autoregressive parameter is invariant over time and lies between-1 and 1, it can be shown that these models are algebraically equivalent. This result can be shown to generalize to the multivariate case. When the autoregressive parameters in the autoregressive latent trajectory model vary over time, the equivalence between the autoregressive latent trajectory model and a latent growth curve model with autoregressive disturbances no longer holds. However, a latent growth curve model with time-varying autoregressive parameters for the disturbances could be considered an interesting alternative to the autoregressive latent trajectory model with time-varying autoregressive parameters.

The present study examined implicit memory transfer in patients with dissociative identity disorder (DID). To determine priming impairments in DID, we included both several perceptual priming tasks and a conceptual priming task using neutral material. We tested a large sample of DID patients (n = 31), in addition to 25 controls and 25 DID simulators, comparable on sex, age, and education. Controls replicated conceptual priming results of Vriezen, Moscovitch, and Bellos (1995) by showing that conceptual priming seems to require the formation of domain-specific semantic representations, denoting either sensory or functional object attributes. We extended a study performed by Schacter, Cooper, and Delaney (1990) by demonstrating priming for impossible object using the sensitive priming index of response times. The simulators in the study were not able to simulate interidentity amnesia on the implicit memory tasks employed. Partly in contrast to participants in previous studies, DID patients showed evidence of perceptual priming as well as conceptual priming comparable to that of controls. DID patients thus displayed normal implicit memory performance.

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