Testing non-nested structural equation models

In this paper, we apply Vuong's (1989) likelihood ratio tests of non-nested models to the comparison of non-nested structural equation models. Similar tests have been previously applied in SEM contexts (especially to mixture models), though the non-standard output required to conduct the tests has limited their previous use and study. We review the theory underlying the tests and show how they can be used to construct interval estimates for differences in non-nested information criteria. Through both simulation and application, we then study the tests' performance in non-mixture SEMs and describe their general implementation via free R packages. The tests offer researchers a useful tool for non-nested SEM comparison, with barriers to test implementation now removed.Comment: 24 pages, 6 figure

Quantifying parsimony in structural equation modeling

Fitting propensity (FP) is defined as a model's average ability to fit diverse data patterns, all else being equal. The relevance of FP to model selection is examined in the context of structural equation modeling (SEM). In SEM it is well known that the number of free model parameters influences FP, but other facets of FP are routinely excluded from consideration. It is shown that models possessing the same number of free parameters but different structures may exhibit different FPs. The consequences of this fact are demonstrated using illustrative examples and models culled from published research. The case is made that further attention should be given to quantifying FP in SEM and considering it in model selection. Practical approaches are suggested

Proportional structural effects of formative indicators

Formative constructs must influence two or more distinct outcome variables for meaningful tests of the formative conceptualization. Because the construct mediates the effects of its indicators, the indicators must have effects on the outcomes that are proportional to their effects on the formative construct itself. This constraint has important implications for developing and testing formative models. This study demonstrates the existence of the constraint, shows that researchers must consider proportionality as a criterion for evaluating the formative conceptualization, provides examples of indicators having different effects and interpretations depending on the outcome variables used, discusses the selection of outcomes to provide rigorous rather than trivial tests of the formative conceptualization, and contends that the formative nature of constructs cannot be justified in isolation from the consideration of outcome variables. In addition, the study demonstrates the importance of considering how the scaling of the formative construct influences the significance of the effects in the model

Similarity in Relationships as Niche Construction: Choice, Stability, and Influence within Dyads in a Free Choice Environment

A series of field studies focused on the role of similarity as niche construction in friendships. Using a free-range dyad harvest method, we collected 11 independent samples with 1,523 interacting pairs, and compared dyad members’ personality traits, attitudes, values, recreational activities, and alcohol and drug use. Within-dyad similarity was statistically significant on 86% of variables measured. To determine whether similarity was primarily due to niche construction (i.e., selection) or social influence, we tested whether similarity increased as closeness, intimacy, discussion, length of relationship, and importance of the attitude increased. There were no effects on similarity of closeness, relationship length, or discussion of the attitude. There were quite modest effects of intimacy, and a reliable effect of the shared importance of the attitude. Because relationship length, intimacy, closeness, and discussion can all serve as markers of opportunity for, or potency of social influence, these data are consistent with the “niche construction” account of similarity. In two follow-up controlled longitudinal field studies, participants interacted with people they did not know from their large lecture classes, and at a later time completed a survey of attitudes, values, and personality traits. Interacting pairs were not more similar than chance, but for the 23% of dyads that interacted beyond the first meeting, there was significant similarity within dyad members. These two lines of inquiry converge to suggest that similarity is mainly due to niche construction, and is most important in the early stages of a relationship; its importance to further relationship development wanes

Exploratory factor analysis in behavior genetics research: Factor recovery with small sample sizes

Results of a Monte Carlo study of exploratory factor analysis demonstrate that in studies characterized by low sample sizes the population factor structure can be adequately recovered if communalities are high, model error is low, and few factors are retained. These are conditions likely to be encountered in behavior genetics research involving mean scores obtained from sets of inbred strains. Such studies are often characterized by a large number of measured variables relative to the number of strains used, highly reliable data, and high levels of communality. This combination of characteristics has special consequences for conducting factor analysis and interpreting results. Given that limitations on sample size are often unavoidable, it is recommended that researchers limit the number of expected factors as much as possible

SPSS and SAS procedures for estimating indirect effects in simple mediation models

Researchers often conduct mediation analysis in order to indirectly assess the effect of a proposed cause on some outcome through a proposed mediator. The utility of mediation analysis stems from its ability to go beyond the merely descriptive to a more functional understanding of the relationships among variables. A necessary component of mediation is a statistically and practically significant indirect effect. Although mediation hypotheses are frequently explored in psychological research, formal significance tests of indirect effects are rarely conducted. After a brief overview of mediation, we argue the importance of directly testing the significance of indirect effects and provide SPSS and SAS macros that facilitate estimation of the indirect effect with a normal theory approach and a bootstrap approach to obtaining confidence intervals, as well as the traditional approach advocated by Baron and Kenny (1986). We hope that this discussion and the macros will enhance the frequency of formal mediation tests in the psychology literature. Electronic copies of these macros may be downloaded from the Psychonomic Society's Web archive at www.psychonomic.org/archive/

Repairing Tom Swift's electric factor analysis machine

Proper use of exploratory factor analysis (EFA) requires the researcher to make a series of careful decisions. Despite attempts by Floyd and Widaman (1995), Fabrigar, Wegener, MacCallum, and Strahan (1999), and others to elucidate critical issues involved in these decisions, examples of questionable use of EFA are still common in the applied factor analysis literature. Poor decisions regarding the model to be used, the criteria used to decide how many factors to retain, and the rotation method can have drastic consequences for the quality and meaningfulness of factor analytic results. One commonly used approach--principal components analysis, retention of components with eigenvalues greater than 1.0, and varimax rotation of these components--is shown to have potentially serious negative consequences. In addition, choosing arbitrary thresholds for factor loadings to be considered large, using single indicators for factors, and violating the linearity assumptions underlying EFA can have negative consequences for interpretation of results. It is demonstrated that, when decisions are carefully made, EFA can yield unambiguous and meaningful results