This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index presentation strategy, which includes using the maximum likelihood (ML)‐based standardized root mean squared residual (SRMR) and supplementing it with either Tucker‐Lewis Index (TLI), Bollen's (1989) Fit Index (BL89), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), Gamma Hat, McDonald's Centrality Index (Mc), or root mean squared error of approximation (RMSEA), various combinations of cutoff values from selected ranges of cutoff criteria for the ML‐based SRMR and a given supplemental fit index were used to calculate rejection rates for various types of true‐population and misspecified models; that is, models with misspecified factor covariance(s) and models with misspecified factor loading(s). The results suggest that, for the ML method, a cutoff value close to .95 for TLI, BL89, CFI, RNI, and G...

Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives

Interest in the problem of method biases has a long history in the behavioral sciences. Despite this, a comprehensive summary of the potential sources of method biases and how to control for them does not exist. Therefore, the purpose of this article is to examine the extent to which method biases influence behavioral research results, identify potential sources of method biases, discuss the cognitive processes through which method biases influence responses to measures, evaluate the many different procedural and statistical techniques that can be used to control method biases, and provide recommendations for how to select appropriate procedural and statistical remedies for different types of research settings.

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Common method biases in behavioral research: a critical review of the literature and recommended remedies.

In this article, we provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests. We discuss the comparative advantages of this approach over a one-step approach. Considerations in specification, assessment of fit, and respecification of measurement models using confirmatory factor analysis are reviewed. As background to the two-step approach, the distinction between exploratory and confirmatory analysis, the distinction between complementary approaches for theory testing versus predictive application, and some developments in estimation methods also are discussed.

/pdf/structural-equation-modeling-in-practice-a-review-and-1ue2omj492.pdf

Structural equation modeling in practice: a review and recommended two-step approach

The unity and diversity of executive functions and their contributions to complex "Frontal Lobe" tasks: a latent variable analysis.

The structure of negative emotional states: comparison of the Depression Anxiety Stress Scales (DASS) with the Beck Depression and Anxiety Inventories.

Fungible Parameter Estimates in Latent Curve Models

Relationships Between LGM and Multilevel Modeling

core matrix, a matrix consisting of as many sections as person dimensions with each section specifying how each person dimension is related to perception of the stimulus dimensions. If all sections of the core matrix are diagonal, or very nearly so, the three-mode solution has the basic form of an INDSCAL solution in the sense that individual differences can be represented in terms of differential

TRINFORM: A Computer Program to Transform a Three-Mode Multidimensional Scaling Solution to INDSCAL Form

In this dissertation, an Expectation-Maximization (EM) algorithm is developed and implemented to obtain maximum likelihood estimates of the parameters and the associated standard error estimates characterizing temporal flows for the latent variable time series following stationary vector ARMA processes, as well as the parameters defining the relationship between the latent stochastic vector and the observed scores taking measurement errors into account. Such models have been known as Process Factor Analysis (PFA) models (Browne & Nesselroade, 2005). In the E-step, the complete-data expected log-likelihood, the so-called Q-function, which is the joint likelihood of the manifest variables and the latent time series process variables, is constructed by supposing the latent process variables are observed. In the M-step, the Newton-Raphson algorithm is employed in order to update the parameter estimates. The closed form expressions for the gradient vector and the Hessian matrix of the target function are derived for implementing the M-step of the EM algorithm. Methods for obtaining the associated standard error estimates are developed and implemented. The proposed EM algorithm employs the covariance structure derived by du Toit and Browne (2007) where the influence of the time series prior to the first observation has remained stable and unchanged when the first observations are made. Thus, unlike other conventional structural equation modeling (SEM) software, model implied covariance matrices satisfy the stability condition and are Block-Toeplitz matrices. The proposed algorithm is applied to simulated data in order to ascertain its viability. Specifically, the recovery of the population parameter values of the proposed EM algorithm is studied with simulated data, which is generated so as to follow a PFA model. The performance of the developing method for standard error estimation is evaluated in the simulation study. The results of the simulation study show that the proposed methods for obtaining parameter estimates and the associated standard error estimates for PFA models can be effectively employed both to single-subject time-series analysis and to repeated time-series analysis. Remaining methodological issues for future research are discussed.

https://cdr.lib.unc.edu/downloads/cr56n1516

Robert C. MacCallum

Papers

Fungible Parameter Estimates in Latent Curve Models

Relationships Between LGM and Multilevel Modeling

TRINFORM: A Computer Program to Transform a Three-Mode Multidimensional Scaling Solution to INDSCAL Form

An em algorithm for maximum likelihood estimation of process factor analysis models

Applying LGM to Empirical Data