Covariance Structure Models Research Articles

The Effect of the Number of Observations per Parameter in Misspecified Confirmatory Factor Analytic Models

Abstract Some authors have suggested that sample size in covariance structure modeling should be considered in the context of how many parameters are to be estimated (e.g., Kline, 2005). Previous research has examined the effect of varying sample size relative to the number of parameters being estimated (N:q). Although some support has been found for this effect, the effect size appears to be small compared to other influences, such as indicator reliability and sample size (Jackson, 2003). Efforts to extend this work to the case where models are intentionally misspecified are described in this article. In addition to varying the number of observations per estimated parameter, several other known influences on model fit were varied such as sample size, the degree of misspecification, number of variables per factor, and the communality of the measured variables. The results suggest that decreasing the number of parameters to be estimated while holding sample size constant can help detect misspecification er...

The Effect of the Number of Observations per Parameter in Misspecified Confirmatory Factor Analytic Models

Some authors have suggested that sample size in covariance structure modeling should be considered in the context of how many parameters are to be estimated (e.g., Kline, 2005). Previous research has examined the effect of varying sample size relative to the number of parameters being estimated (N:q). Although some support has been found for this effect, the effect size appears to be small compared to other influences, such as indicator reliability and sample size (Jackson, 2003). Efforts to extend this work to the case where models are intentionally misspecified are described in this article. In addition to varying the number of observations per estimated parameter, several other known influences on model fit were varied such as sample size, the degree of misspecification, number of variables per factor, and the communality of the measured variables. The results suggest that decreasing the number of parameters to be estimated while holding sample size constant can help detect misspecification errors, and some fit indexes were more sensitive to this manipulation than others. In general, the effects of N:q were small relative to other experimental effects.

Examining Temporal Stability of Scale Validity in Longitudinal Studies

A method for examining invariance in validity of multiple-component instruments in repeated measure designs is outlined. The approach is developed within the framework of covariance structure modeling and is applicable for purposes of ascertaining temporal stability in scale validity. In addition, the procedure provides a range ofplausible values in a population under investigation for the change in composite validity across longitudinal assessment occasions. The proposed method can also be used to examine possible sources of lack of validity invariance, and is illustrated with a pair of examples.

Measurement of psychological disorders using cognitive diagnosis models.

Cognitive diagnosis models are constrained (multiple classification) latent class models that characterize the relationship of questionnaire responses to a set of dichotomous latent variables. Having emanated from educational measurement, several aspects of such models seem well suited to use in psychological assessment and diagnosis. This article presents the development of a new cognitive diagnosis model for use in psychological assessment--the DINO (deterministic input; noisy "or" gate) model--which, as an illustrative example, is applied to evaluate and diagnose pathological gamblers. As part of this example, a demonstration of the estimates obtained by cognitive diagnosis models is provided. Such estimates include the probability an individual meets each of a set of dichotomous Diagnostic and Statistical Manual of Mental Disorders (text revision [DSM-IV-TR]; American Psychiatric Association, 2000) criteria, resulting in an estimate of the probability an individual meets the DSM-IV-TR definition for being a pathological gambler. Furthermore, a demonstration of how the hypothesized underlying factors contributing to pathological gambling can be measured with the DINO model is presented, through use of a covariance structure model for the tetrachoric correlation matrix of the dichotomous latent variables representing DSM-IV-TR criteria.

The Performance of Cross-Validation Indices Used to Select Among Competing Covariance Structure Models Under Multivariate Nonnormality Conditions

Cudeck and Browne (1983) proposed using cross-validation as a model selection technique in structural equation modeling. The purpose of this study is to examine the performance of eight cross-validation indices under conditions not yet examined in the relevant literature, such as nonnormality and cross-validation design. The performance of each cross-validation index was measured in terms of true model selection rate as well as consistency of model selection. The performance of the cross-validation indices tended to improve as factor loading and sample size increased but performed less well as nonnormality increased. The double cross-validated indices outperformed their simple cross-validated counterparts in certain conditions. Recommendations are provided as to which cross-validation methods would optimally perform in a given condition.

Comparing Fixed Effects and Covariance Structure Estimators for Panel Data

In this article, the authors compare the traditional econometric fixed effect estimator with the maximum likelihood estimator implied by covariance structure models for panel data. Their findings are that the maximum like lipoid estimator is remarkably robust to certain types of misspecifications (e.g., deviation from the assumption of an underlying normal distribution). However, with other types of misspecification, the fixed estimator is pre ferable. Furthermore, the authors suggest that the Hausman specification test may be used as a test of the consistency of the maximum likelihood estimator.

Maximal reliability and power in covariance structure models

In covariance structure modelling, the non-centrality parameter of the asymptotic chi-squared distribution is typically used as an indicator of asymptotic power for hypothesis tests. When a latent linear regression is of interest, the contribution to power by the maximal reliability coefficient, which is associated with used latent variable indicators, is examined and this relationship is further explicated in the case of congeneric measures. It is also shown that item parcelling may reduce power of tests of latent regression parameters. Recommendations on weights for parcelling to avoid power loss are provided, which are found to be those of optimal linear composites with maximal reliability.

Relationships of retail brand manufacturers with retailers

Previous researchers have discussed the convenience of manufacturing retail brands. However, they have seldom developed any empirical work. In this article we present an analysis framework to study the impact of the production of retail brands on the manufacturer's relationship with the retailer, depending on the manufacturer's competitive position in the brands they produce. The model presented is empirically tested through a covariance structure model. In order to do this, we use the data from a postal survey aimed at business units manufacturing retail brands in the Spanish market for mass commodity products.

A Direct Method for Obtaining Approximate Standard Error and Confidence Interval of Maximal Reliability for Composites With Congeneric Measures

Unlike a substantial part of reliability literature in the past, this article is concerned with weighted combinations of a given set of congeneric measures with uncorrelated errors. The relationship between maximal coefficient alpha and maximal reliability for such composites is initially dealt with, and it is shown that the former is a lower bound of the latter. A direct method for obtaining approximate standard error and confidence interval for maximal reliability is then outlined. The procedure is based on a second-order Taylor series approximation and is readily and widely applicable in empirical research via use of covariance structure modeling. The described method is illustrated with a numerical example.

Testing differences between nested covariance structure models: Power analysis and null hypotheses.

For comparing nested covariance structure models, the standard procedure is the likelihood ratio test of the difference in fit, where the null hypothesis is that the models fit identically in the population. A procedure for determining statistical power of this test is presented where effect size is based on a specified difference in overall fit of the models. A modification of the standard null hypothesis of zero difference in fit is proposed allowing for testing an interval hypothesis that the difference in fit between models is small, rather than zero. These developments are combined yielding a procedure for estimating power of a test of a null hypothesis of small difference in fit versus an alternative hypothesis of larger difference.

Lagged covariance structure models for studying functional connectivity in the brain

Most cognitive processes are supported by large networks of brain regions. To describe the operation of these networks, it is critical to understand how individual areas are functionally connected. Here, we establish a statistical framework for studying effective and functional brain connectivity, using data obtained with a relatively new neuroimaging method, the event-related optical signal (EROS). The novelty of our approach is the use of timing information (in the form of lagged cross-correlations) in interpreting the connections between areas. Interpretation of lagged cross-correlations exploits the combination of spatial and temporal resolution provided by EROS. In this paper, we apply dynamic factor analysis as a method for testing various structural models on the lagged covariance matrices derived from the EROS data. We first illustrate the approach by testing a simple path model of neural activity propagation from area V1 to V3 in a visual stimulation task. We then build more complex structural equation models with latent variables, describing both within-hemisphere integrity, and interactions between the two hemispheres, to interpret data from a second task involving inter-hemispheric competition. The results demonstrate how the integrity of anatomical connections between the two hemispheres explains different patterns of cross-hemispheric interactions. This approach allows for fitting brain imaging data to complex models that capture dynamic cognitive processes as they rapidly evolve over time.

The Rationale of Variation in Methodological and Evidential Pluralism

Causal analysis in the social sciences takes advantage of a variety of methods and of a multi-fold source of information and evidence. The first developments of quantitative causal analysis in the social sciences are due to Quetelet (1869) and Durkheim (1895 and 1897) in demography and sociology respectively. Significant improvements are due to Blalock (1964) and Duncan (1975). Since then causal analysis has shown noteworthy progress in the formal methods of analysis, e.g., structural equation models, covariance structure models, multilevel models, and contingency tables. By means of these different methodologies, social scientists try to infer causal relations between variables of interest with reasonable confidence. Data comes from a variety of different sources: surveys, census, experiments, interviews, etc. Analogously, evidence of causal relations can come from different sources: previous studies, background knowledge, knowledge of mechanisms or of probabilistic relations, etc. This pluralistic methodology and source of information raises the question of whether we should accordingly have a pluralistic metaphysics and epistemology. This paper focuses on epistemology and argues that a pluralistic methodology and evidence do not entail a pluralistic epistemology. It will be shown that causal models employ a single rationale of testing, based on the notion of variation. This view of causality profoundly breaks down with the received view, an heritage of Hume, that sees in regularity and/or invariance the key notions for causality. For instance, the rationale of variation clearly emerges in the interpretation of structural equation models: given a system of equations, parameters quantify the variation of the dependent variable due to the variation in the independent variable(s). Regularity and invariance thus become constraints to impose on the variation in order ensure that the model correctly specify the data generating process and that it does not confuse accidental and spurious relations with causal ones. Further, I argue that this monistic epistemology is also involved in alternative philosophical theories of causation, for instance, in probabilistic theories of causality, mechanist and counterfactual accounts, agency-manipulability theories and in the epistemic theory. The philosophical gain in adopting the rationale of variation is at least threefold. First, causality is not merely lodged in a psychological habit of observing regular successions of events. Agreed, we do experience such regular sequences but it is not because of regularity that we interpret them causally. Instead, this is because certain variational relations hold. Second, causality is not reduced to statistics either. Further, to claim that variation is a precondition for regularity and invariance has the advantage of not confusing the rationale of causality with the conditions that allow to interpret variations causally. Third, the adoption of the rationale of variation avoids confusing (i) what causality is (metaphysics) with the notion employed in testing (epistemology) and (ii) with the conditions – e.g. invariance – to impose on the variation to interpret it causally (methodology).

Mixture of Covariance Structure Models to Identify Different Types of Life Style

A central topic of empirical social research is the problem of unobserved heterogeneity. To solve this problem at least partially, a statistical model is presented: the finite mixture of conditional mean and covariance structure models. In this approach, the expected values in each component of a mixture may depend on normally or nonnormally distributed regressor variables. The expected value and the covariance matrix in each component of the mixture are parameterized using conditional mean and covariance structure models. Three different procedures for estimating the parameters of these models are briefly discussed. The model and the estimation procedures are applied to data of the German General Social Survey 1998 to identify heterogenous types of life style. Since different regression models with latent variables may be used for each type, it is not only possible to cover different types of life style, but also different types of relationships between life style dimensions and the influences of sociodemographic variables on life style.

Predicting intentions for long-term anabolic-androgenic steroid use among men: A covariance structure model.

Long-term use of anabolic-androgenic steroids (AASs) is associated with both positive and negative effects. The authors examined possible mechanisms by which these effects contribute to AAS satisfaction and predict intentions for future AAS use. Five hundred male AAS users completed an interactive Web-based instrument assessing the psychological and physical effects of AAS use. Covariance structure modeling was used to evaluate both direct and indirect effects of AAS consequences on satisfaction with AASs and intentions for future AAS use. Results suggest that gain in muscle mass and psychological benefits from AAS use uniquely contributed to both AAS satisfaction and intentions for future use. Side effects from AAS use also uniquely contributed to AAS satisfaction, but ancillary drug use was found to partially mediate this relationship, suggesting that the satisfaction of experienced AAS users is enhanced by their mastery of side effects through the use of ancillary drugs. The final model explained 29% of the variance in intentions for future AAS use. Mechanisms for sustained AAS use and implications for intervention and prevention strategies are discussed.

A Covariance Structure Model for Factors Related to Social Activities of the Elderly Living at Home

A Covariance Structure Model for Factors Related to Social Activities of the Elderly Living at Home

Supplemental Material for Testing Differences Between Nested Covariance Structure Models: Power Analysis and Null Hypotheses

Supplemental Material for Testing Differences Between Nested Covariance Structure Models: Power Analysis and Null Hypotheses

Internet users' attitude and behavioural intention on ebranding

The purpose of this paper is to empirically examine the effect of internet users' general attitude towards internet advertising and level of product involvement on their attitudes and behaviour. In this study, three banner advertisements and corporate websites of varying creative content and message appeal were used. Data was gathered through an online survey with a sample size of 245 respondents. The Covariance Structural Modelling results show that general attitude towards internet advertising and level of product involvement has a positive impact on users' attitudes (site and brand) and behavioural intention. The results show that the extent to which users perceive a corporate website is customised from information derived from their individual-level differences and is influenced by their general attitude towards internet advertising and level of involvement.

On Multilevel Model Reliability Estimation From the Perspective of Structural Equation Modeling

A covariance structure modeling perspective on reliability estimation can be used to construct a formal approach to estimation of reliability in multilevel models. This article presents a didactic discussion of the relation between a structural modeling procedure for scale reliability estimation and the notion of reliability of observed means in unconditional multilevel models. The utility of the method is demonstrated as an alternative means for conceptualizing multilevel modeling reliability. The relationship between the underlying two reliability notions is illustrated on a set of hierarchical data.

Probabilistic and Ensemble Representations of the Uncertainty in an IR/Microwave Satellite Precipitation Product

AbstractWhile current satellite techniques are theoretically capable of producing precipitation estimates to image pixel resolutions, significant uncertainty is present in such high-resolution products. This uncertainty is frequently difficult to characterize using scalar measures of additive error. This paper describes the development of a methodology to more fully represent the uncertainty in satellite precipitation retrievals. The methodology derives conditional probability distribution functions of rainfall on a pixel-by-pixel basis. This array of distribution functions is then combined with a simple model of the spatiotemporal covariance structure of the uncertainty in the precipitation field to stochastically generate an ensemble precipitation product. Each element of the ensemble represents an equiprobable realization of the precipitation field that is consistent with the original satellite data while containing a random element commensurate with the uncertainty in that field. The technique has been tested using data from the Tropical Rainfall Measuring Mission (TRMM) Texas and Florida Underflight Experiment (TEFLUN-B) field campaign.

Illness burden mediates the relationship between pain and illicit drug use in persons living with HIV

We investigated predictive and concurrent relationships among reported pain, HIV/AIDS illness burden, and substance use history in 2267 participants in the longitudinal HIV Cost and Services Utilization Study (HCSUS). Substance use history was classified as screening positive for current illicit drug use ( N=253), past drug use ( N=617), and non-user ( N=1397) at baseline. To control for demographic correlates, age, sex and socioeconomic status (SES) were included as predictors. Covariance structure models indicated greater pain at baseline among participants acknowledging current substance use. Pain at baseline was also directly predicted by greater HIV/AIDS illness burden, lower SES, and older age. At 6 months, pain was directly predicted by prior pain, worse concurrent HIV/AIDS illness burden and female sex. At 12 months, pain was predicted by older age, prior pain, and concurrent HIV/AIDS illness. It was also modestly but significantly predicted by current substance use at baseline. In addition to the direct effects on pain, there were significant indirect effects of demographic and drug use variables on pain mediated through HIV/AIDS illness burden and prior pain. There were significant and positive indirect effects of current and past drug use, greater age, and lower SES on pain at all three time periods. Pain at 6 months and pain at 12 months were also indirectly impacted by previous illness burden. Our results indicate that HIV+persons who screened positive for current use of a range of illicit substances experienced greater HIV/AIDS illness burden which in turn predicted increased pain.