Transformation of a three-mode multidimensional scaling solution to indscal form

Relations between Tucker's three-mode multidimensional scaling and Carroll and Chang's INDSCAL are discussed. The possibility is raised that it may be profitable to attempt to transform a three-mode solution to the general form of an INDSCAL solution. Operationally, this involves transforming the three-mode core matrix so that each section is, as nearly as possible, a diagonal matrix. A technique is developed for accomplishing such a transformation, and is applied to two sets of data from the literature. Results indicate that the process is both feasible and valuable, providing useful information on the relative appropriateness of the two models.     

Families created through surrogacy arrangements: parent-child relationships in the 1st year of life

Findings are presented of a study of families created through surrogacy arrangements. Forty-two surrogacy families were compared with 51 egg-donation families and 80 natural-conception families on standardized interview and questionnaire measures of the psychological well-being of the parents, the quality of parent-child relationships, and infant temperament. The differences that were identified between the surrogacy families and the other family types indicated greater psychological well-being and adaptation to parenthood by mothers and fathers of children born through surrogacy arrangements than by the natural-conception parents.     

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.     

Sensitivity Analysis in Structural Equation Models: Cases and Their Influence

The detection of outliers and influential observations is routine practice in linear regression. Despite ongoing extensions and development of case diagnostics in structural equation models (SEM), their application has received limited attention and understanding in practice. The use of case diagnostics informs analysts of the uncertainty of model estimates under different subsets of the data and highlights unusual and important characteristics of certain cases. We present several measures of case influence applicable in SEM and illustrate their implementation, presentation, and interpretation with two empirical examples: (a) a common factor model on verbal and visual ability (Holzinger &; Swineford, 1939 Holzinger, K. and Swineford, F. 1939. A study in factor analysis: The stability of a bi-factor solution. Chicago, IL: University of Chicago..  [Google Scholar]) and (b) a general structural equation model assessing the effect of industrialization on democracy in a mediating model using country-level data (Bollen, 1989 Bollen, K. A. 1989. Structural equation models with latent variables New York, NY: Wiley.. [Crossref] , [Google Scholar]; Bollen &; Arminger, 1991 Bollen, K. A. and Arminger, G. 1991. Observational residuals in factor analysis and structural equation models. Sociological Methodology, 21: 235–262. [Crossref], [Web of Science ®] , [Google Scholar]). Throughout these examples, three issues are emphasized. First, cases may impact different aspects of results as identified by different measures of influence. Second, the important distinction between outliers and influential cases is highlighted. Third, the concept of good and bad cases is introduced—these are influential cases that improve/worsen overall model fit based on their presence in the sample. We conclude with a discussion on the utility of detecting influential cases in SEM and present recommendations for the use of measures of case influence.     

A comparison of factor analysis programs in SPSS,BMDP, and SAS

Factor analysis programs in SAS, BMDP, and SPSS are discussed and compared in terms of documentation, methods and options available, internal logic, computational accuracy, and results provided. Some problems with respect to logic and output are described. Based on these comparisons, recommendations are offered which include a clear overall preference for SAS, and advice against general use of SPSS for factor analysis.     

Effects of conditionality on INDSCAL and ALSCAL weights

The role of conditionality in the INDSCAL and ALSCAL procedures is explained. The effects of conditionality on subject weights produced by these procedures is illustrated via a single set of simulated data. Results emphasize the need for caution in interpreting subject weights provided by these techniques.     

On the practice of dichotomization of quantitative variables

The authors examine the practice of dichotomization of quantitative measures, wherein relationships among variables are examined after 1 or more variables have been converted to dichotomous variables by splitting the sample at some point on the scale(s) of measurement. A common form of dichotomization is the median split, where the independent variable is split at the median to form high and low groups, which are then compared with respect to their means on the dependent variable. The consequences of dichotomization for measurement and statistical analyses are illustrated and discussed. The use of dichotomization in practice is described, and justifications that are offered for such usage are examined. The authors present the case that dichotomization is rarely defensible and often will yield misleading results.     

Effects on indscal of non-orthogonal perceptions of object space dimensions

A general question is raised concerning the possible consequences of employing the very popular INDSCAL multidimensional scaling model in cases where the assumptions of that model may be violated. Simulated data are generated which violate the INDSCAL assumption that all individuals perceive the dimensions of the common object space to be orthogonal. INDSCAL solutions for these various sets of data are found to exhibit extremely high goodness of fit, but systematically distorted object spaces and negative subject weights. The author advises use of Tucker's three-mode model for multidimensional scaling, which can account for non-orthogonal perceptions of the object space dimensions. It is shown that the INDSCAL model is a special case of the three-mode model.     

A multilevel approach to the relationship between birth order and intelligence

Many studies show relationships between birth order and intelligence but use cross-sectional designs or manifest other threats to internal validity. Multilevel analyses with a control variable show that when these threats are removed, two major results emerge: (a) birth order has no significant influence on children's intelligence and (b) earlier reported birth order effects on intelligence are attributable to factors that vary between, not within, families. Analyses on 7- to 8 - and 13- to 14-year-old children from the National Longitudinal Survey of Youth support these conclusions. When hierarchical data structures, age variance of children, and within-family versus between-family variance sources are taken into account, previous research is seen in a new light.     

When fit indices and residuals are incompatible

Standard chi-square-based fit indices for factor analysis and related models have a little known property: They are more sensitive to misfit when unique variances are small than when they are large. Consequently, very small correlation residuals indicating excellent fit can be accompanied by indications of bad fit by the fit indices when unique variances are small. An empirical example of this incompatibility between residuals and fit indices is provided. For illustrative purposes, an artificial example is provided that yields exactly the same correlation residuals as the empirical example but has larger unique variances. For this example, the fit indices indicate excellent fit. A theoretical explanation for this phenomenon is provided using relationships between unique variances and eigenvalues of the fitted correlation matrix.