Subclmical depression and role fulfillment in domestic settings: Spurious relationships,imagined problems,or real effects?

Considerable evidence has accumulated in support of the hypothesis that subclinical depression may inhibit role performance in important ways. However, interpersonal stress and marital discord often precede the development of depressive symptomatology and may independently predict deficits in family role functioning. In addition, cognitive theories suggest that persons with subclinical depression may report poor role functioning even in the absence of any real performance deficits. The current research examines the possibility (1) that the effect of depression on the fulfillment of important family roles is attributable to previously unmeasured contextual variables of ongoing interpersonal stress and/or relationship dissatisfaction or, alternatively, (2) that this relationship is the result of depressive distortion associated with self-report of symptoms and performance. Multiple regression analyses of interview data collected from 495 community-dwelling adults found, however, that depression is related to role functioning beyond any spurious effects attributable to interpersonal stress, spousal stress, or marital satisfaction. In addition, the effect of depression persists when collateral reports of role functioning utilized. Accordingly, it appears that subclinical depression is related to decrements in role performance, and this effect is not entirely due to contextual elements or shared method variance between self-report measures.The authors acknowledge research support from Research Grants R01-AA-07250 and R01-AA-07218 from the National Institute on Alcohol Abuse and Alcoholism, Research Grant R01-DA-07417 from the National Institute on Drug Abuse, and National Institutes of Mental Health Grant A-41487-07.     

Adjusting for information inflation due to local dependency in moderately large item clusters

When multiple items are clustered around a reading passage, the local independence assumption in item response theory is often violated. The amount of information contained in an item cluster is usually overestimated if violation of local independence is ignored and items are treated as locally independent when in fact they are not. In this article we provide a general method that adjusts for the inflation of information associated with a test containing item clusters. A computational scheme was presented for the evaluation of the factor of adjustment for clusters in the restrictive case of two items per cluster, and the general case of more than two items per cluster. The methodology was motivated by a study of the NAEP Reading Assessment. We present a simulated study along with an analysis of a NAEP data set.The research was supported under the National Assessment of Educational Progress (Grant No. R999G30002) as administered by the Office of Educational Research and Improvement, U.S. Department of Education. This work was started when the author was at the Division of Statistics and Psychometrics at the Educational Testing Service. The author thanks Juliet Shaffer, Bob Mislevy, Eric Bradlow, three reviewers and an associate editor for their helpful comments on the paper.     

Comparative evaluation of two superior stopping rules for hierarchical cluster analysis

A split-sample replication stopping rule for hierarchical cluster analysis is compared with the internal criterion previously found superior by Milligan and Cooper (1985) in their comparison of 30 different procedures. The number and extent of overlap of the latent population distributions was systematically varied in the present evaluation of stopping-rule validity. Equal and unequal population base rates were also considered. Both stopping rules correctly identified the actual number of populations when there was essentially no overlap and clusters occupied visually distinct regions of the measurement space. The replication criterion, which is evaluated by clustering of cluster means from preliminary analyses that are accomplished on random partitions of an original data set, was superior as the degree of overlap in population distributions increased. Neither method performed adequately when overlap obliterated visually discernible density nodes.This research was supported in part by NIMH grant 5R01 MH 32457 14.     

Ignoring Clustering in Confirmatory Factor Analysis: Some Consequences for Model Fit and Standardized Parameter Estimates

In many situations, researchers collect multilevel (clustered or nested) data yet analyze the data either ignoring the clustering (disaggregation) or averaging the micro-level units within each cluster and analyzing the aggregated data at the macro level (aggregation). In this study we investigate the effects of ignoring the nested nature of data in confirmatory factor analysis (CFA). The bias incurred by ignoring clustering is examined in terms of model fit and standardized parameter estimates, which are usually of interest to researchers who use CFA. We find that the disaggregation approach increases model misfit, especially when the intraclass correlation (ICC) is high, whereas the aggregation approach results in accurate detection of model misfit in the macro level. Standardized parameter estimates from the disaggregation and aggregation approaches are deviated toward the values of the macro- and micro-level standardized parameter estimates, respectively. The degree of deviation depends on ICC and cluster size, particularly for the aggregation method. The standard errors of standardized parameter estimates from the disaggregation approach depend on the macro-level item communalities. Those from the aggregation approach underestimate the standard errors in multilevel CFA (MCFA), especially when ICC is low. Thus, we conclude that MCFA or an alternative approach should be used if possible.     

Biases in multilevel analyses caused by cluster-specific fixed-effects imputation

When datasets are affected by nonresponse, imputation of the missing values is a viable solution. However, most imputation routines implemented in commonly used statistical software packages do not accommodate multilevel models that are popular in education research and other settings involving clustering of units. A common strategy to take the hierarchical structure of the data into account is to include cluster-specific fixed effects in the imputation model. Still, this ad hoc approach has never been compared analytically to the congenial multilevel imputation in a random slopes setting. In this paper, we evaluate the impact of the cluster-specific fixed-effects imputation model on multilevel inference. We show analytically that the cluster-specific fixed-effects imputation strategy will generally bias inferences obtained from random coefficient models. The bias of random-effects variances and global fixed-effects confidence intervals depends on the cluster size, the relation of within- and between-cluster variance, and the missing data mechanism. We illustrate the negative implications of cluster-specific fixed-effects imputation using simulation studies and an application based on data from the National Educational Panel Study (NEPS) in Germany.     

Sequential validation of cluster analytic subtypes of homeless veterans

To identify subgroups within the homeless population, a number of researchers have employed cluster analytic statistical procedures. Although this is an appropriate application of cluster analysis, many studies have not employed important statistical safeguards against arbitrary results. This study demonstrates a cluster analytic procedure—sequential validation—that enhances the replicability, external validity, and cross-validity of cluster solutions. The procedure is applied to a nationwide sample of 745 homeless veterans. After 12 different clustering procedures were subjected to derivation, replication, external validation, and cross-validation phases, a 4-cluster Ward solution emerged as the most sound. Substantively, the clusters were an alcoholic subtype, a psychiatrically impaired subtype, a best functioning subtype, and a multiproblem subtype. The generalizability of these subgroups to other contexts was assessed by comparing them to subgroups identified in other homelessness research. Suggestions were made for improving the quality of cluster analytic research in community psychology.     

The advantages of mathematical modeling over traditional methods in the analysis of category clustering

A mathematical model for the analysis of category clustering is developed and testd. The model, which can be applied to categories of any size, is an extension of a two-item statistical model developed by Batchelder and Riefer (Psychological Review, 1980, 87, 375–397), and is equivalent to their model when categories consist of two items. The model is based on a current theory of clustering which postulates that the learning of a list of category items occurs on different hierarchical levels. Two category list-learning experiments are presented, and the data from these experiments are analyzed using the general statistical model. The first experiment reveals that the probabilities of storing and retrieving a cluster increase with category size, while the learning of items as singletons decreases. The effects of within-category spacing indicate that the storage of clusters decreases while cluster retrievability increases with an increase in input spacing. In the second experiment, the storage and retrieval of clusters are shown to be unaffected by whether the presentation of items is uncued or cued with the name of the category. However, the association of items decreases and the learning of items as singletons increases with uncued presentation. In the final sections, the general statistical model is compared to other methods for the measurement of category clustering. The model is shown to be superior to numerical indices of clustering, since these measures are not based on any theory of clustering, and because unitary measures cannot capture the multiprocess nature of categorized recall. The model is also argued to have certain advantages over other mathematical models that have been applied to category clustering, since these models cannot account for situations in which a portion of the items are clustered while others are learned singularly.     

A unified approach to exploratory factor analysis with missing data,nonnormal data,and in the presence of outliers

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.This project was supported by a University of North Texas Faculty Research Grant, Grant #R49/CCR610528 for Disease Control and Prevention from the National Center for Injury Prevention and Control, and Grant DA01070 from the National Institute on Drug Abuse. The results do not necessarily represent the official view of the funding agencies. The authors are grateful to three reviewers for suggestions that improved the presentation of this paper.     

Some statistical considerations in multidimensional scaling

Some shortcomings of current methods of estimating the magnitude of perceived difference are considered. A statistical model for perceived difference is derived which avoids these difficulties and employs judgments of ratios of differences as data. Three estimators of squared difference are developed.This study was conducted while the author was a Psychometric Fellow at Princeton University and Educational Testing Service and is part of a dissertation presented in candidacy for the degree of doctor of philosophy. This research was supported by Office of Naval Research Contract Nonr 1858 and by National Science Foundation Grant GB3402. Extensive use was made of the computing facilities of Princeton University supported in part by National Science Foundation Grant NSF-GP579. The author wishes to express his appreciation to Prof. H. Gulliksen, Prof. F. Geldard, Dr. C. Helm, and Dr. F. Lord for their comments and encouragement.     

Cautionary Remarks on the Use of Clusterwise Regression

Clusterwise linear regression is a multivariate statistical procedure that attempts to cluster objects with the objective of minimizing the sum of the error sums of squares for the within-cluster regression models. In this article, we show that the minimization of this criterion makes no effort to distinguish the error explained by the within-cluster regression models from the error explained by the clustering process. In some cases, most of the variation in the response variable is explained by clustering the objects, with little additional benefit provided by the within-cluster regression models. Accordingly, there is tremendous potential for overfitting with clusterwise regression, which is demonstrated with numerical examples and simulation experiments. To guard against the misuse of clusterwise regression, we recommend a benchmarking procedure that compares the results for the observed empirical data with those obtained across a set of random permutations of the response measures. We also demonstrate the potential for overfitting via an empirical application related to the prediction of reflective judgment using high school and college performance measures.     

A theory of appropriate statistics

A formal theory of appropriateness for statistical operations is presented which incorporates features of Stevens' theory of appropriate statistics and Suppes' theory of empirical meaningfulness. It is proposed that a statistic be regarded as appropriate relative to statements made about it in case the truths of these statements are invariant under permissible transformations of the measurement scale. It is argued that the use of inappropriate statistics leads to the formulation of statements which are either semantically meaning-less or empirically nonsignificant.This research was supported in part by each of the following grants: National Science Foundation Grant GS-333 to the University of Oregon; National Science Foundation Grant to the Institute of Human Learning, University of California, Berkeley; and National Institute of Mental Health Grant MH-08055-01 (under the direction of Ernest W. Adams), also to the Institute of Human Learning. Work on this project was carried out in part during Robert F. Fagot's tenure as Public Health Service Special Fellow (No. MSP-15800) at the University of California, Berkeley, 1962-63; and during Richard E. Robinson's tenure as National Science Foundation Science Faculty Fellow at Stanford University, 1962–63.     

Statistical inference in generalized linear mixed models: A review

We present a review of statistical inference in generalized linear mixed models (GLMMs). GLMMs are an extension of generalized linear models and are suitable for the analysis of non‐normal data with a clustered structure. A GLMM contains parameters common to all clusters (fixed regression effects and variance components) and cluster‐specific parameters. The latter parameters are assumed to be randomly drawn from a population distribution. The parameters of this population distribution (the variance components) have to be estimated together with the fixed effects. We focus on the case in which the cluster‐specific parameters are normally distributed. The cluster‐specific effects are integrated out of the likelihood so that the fixed effects and variance components can be estimated. Unfortunately, the integral over the cluster‐specific effects is intractable for most GLMMs with a normal mixing distribution. Within a classical statistical framework, we distinguish between two broad classes of methods to handle this intractable integral: methods that rely on a numerical approximation to the integral and methods that use an analytical approximation to the integrand. Finally, we present an overview of available methods for testing hypotheses about the parameters of GLMMs.     

The parish clergy as a mental health resource

Summary This paper presents observations on the assets and liabilities of the parish clergy as a mental health resource within the community. These observations are drawn from a ten-year program of continuing education for cleargy in mental health, which focuses on daily pastoral experience. The parish setting is similar in many respects to the service area of a community mental health center. The clergy's assets often include availability, experience, tradition, and the special significance of the religious leader. Inadequate training in mental health skills and the complex demands of parish life are among the problems confronting the clergy in this area. On the whole, the pastoral role offers a unique and highly useful opportunity for positive psychological intervention.The work described in this paper has been supported in part by National Institute of Mental Health grant no. MH-11929-01 and by grants from the Cleveland Foundation and the Grant Foundation, Inc., and the Cuyahoga County Board of Mental Health and Mental Retardation.     

Finding groups using model-based cluster analysis: heterogeneous emotional self-regulatory processes and heavy alcohol use risk

Model-based cluster analysis is a new clustering procedure to investigate population heterogeneity utilizing finite mixture multivariate normal densities. It is an inferentially based, statistically principled procedure that allows comparison of nonnested models using the Bayesian information criterion to compare multiple models and identify the optimum number of clusters. The current study clustered 36 young men and women on the basis of their baseline heart rate and heart rate variability (HRV), chronic alcohol use, and reasons for drinking. Two cluster groups were identified and labeled the high alcohol risk and normative groups. Compared to the normative group, individuals in the high alcohol risk group had higher levels of alcohol use and more strongly endorsed disinhibition and suppression reasons for use. The high alcohol risk group showed significant HRV changes in response to positive and negative emotional and appetitive picture cues, compared to neutral cues. In contrast, the normative group showed a significant HRV change only to negative cues. Findings suggest that individuals with autonomic self-regulatory difficulties may be more susceptible to heavy alcohol use and use of alcohol for emotional regulation.     

On the Cross‐Cultural Replicability of the Resilient,Undercontrolled, and Overcontrolled Personality Types

Personality types reflect typical configurations of personality attributes within individuals. Over the last 20 years, researchers have identified a set of three replicable personality types: resilient (R), undercontrolled (U), and overcontrolled (O) types. In this study, we examined the cross‐cultural replicability of the RUO types in Italy, Poland, Spain, and the United States. Personality types were identified using cluster analyses of Big Five profiles in large samples of college students from Italy (n = 322), the United States (n = 499), Spain (n = 420), and Poland (n = 235). Prior to clustering the profiles, the measurement invariance of the Big Five measure across samples was tested. We found evidence for the RUO types in all four samples. The three‐cluster solution showed a better fit over alternative solutions and had a relatively high degree of cross‐cultural generalizability. The RUO types are evident in samples from four countries with distinct linguistic and cultural traditions. Results were discussed in light of the importance of considering how traits are organized within individuals for advancing contemporary personality psychology.     

The linear regression line as a judgmental aid in visual analysis of serially dependent A-B time-series data

The purpose of this study was to investigate the effects of different types and magnitudes of serial dependence (first-order moving average and autoregression) and of linear regression lines within experimental phases on the agreement between results of visual and results of statistical data analyses. The stimulus material consisted of computer-simulated A-B-design data graphs. The time series were generated with a constant variance, varying degrees of treatment effects (changes in level), five conditions of serial dependency, and with or without linear regression lines. The material was presented to three groups of student raters (n₁=52, n₂=14, n₃=17) who rated the treatment effect in the graphs on a five-point scale. These ratings were compared with statistical results (time-series analyses). Each group had to interpret 70 graphs, 35 of which had regression lines. Data were analyzed by means of two three-factor and one four-factor ANOVA and by graphic display. The linear regression lines generally enhanced the agreement between the raters' estimations and the statistical results. Serial dependency also increased the agreement between the two analysis methods. However, with strong autoregression processes in the data, the raters tended to overestimate treatment effects relative to time-series analysis.Parts of this study were presented at the World Congress on Behavior Therapy, Washington, DC, December 11, 1983. The authors wish to express their appreciation to Christoph Bonk and Willi Ecker for their extensive collaboration in data analysis and for their assistance in carrying out the study.     

Stability analysis in K‐means clustering

This paper develops a new procedure, called stability analysis, for K‐means clustering. Instead of ignoring local optima and only considering the best solution found, this procedure takes advantage of additional information from a K‐means cluster analysis. The information from the locally optimal solutions is collected in an object by object co‐occurrence matrix. The co‐occurrence matrix is clustered and subsequently reordered by a steepest ascent quadratic assignment procedure to aid visual interpretation of the multidimensional cluster structure. Subsequently, measures are developed to determine the overall structure of a data set, the number of clusters and the multidimensional relationships between the clusters.     

Barriers to Computerized Career Interventions in Community Outreach Centers

This study used a survey design to investigate if computer experience and computer attitudes influence whether economically marginalized individuals desire access to computerized career services in community outreach centers. The majority (84%) of the sample reported a desire for access to computerized career services at community outreach centers. A multiple regression analysis indicated computer attitudes as most predictive of intention to use computerized career services (β = .29, p < .01). Results support extending access to computerized career services in community outreach centers to meet the needs of economically marginalized individuals.     

Cluster randomized trials with treatment noncompliance

Cluster randomized trials (CRTs) have been widely used in field experiments treating a cluster of individuals as the unit of randomization. This study focused particularly on situations where CRTs are accompanied by a common complication, namely, treatment noncompliance or, more generally, intervention nonadherence. In CRTs, compliance may be related not only to individual characteristics but also to the environment of clusters individuals belong to. Therefore, analyses ignoring the connection between compliance and clustering may not provide valid results. Although randomized field experiments often suffer from both noncompliance and clustering of the data, these features have been studied as separate rather than concurrent problems. On the basis of Monte Carlo simulations, this study demonstrated how clustering and noncompliance may affect statistical inferences and how these two complications can be accounted for simultaneously. In particular, the effect of the intervention on individuals who not only were assigned to active intervention but also abided by this intervention assignment (complier average causal effect) was the focus. For estimation of intervention effects considering noncompliance and data clustering, an ML-EM estimation method was employed.