A statistical analysis system (SAS) computer program for Markov chain analysis

A computer program for Markov chain analysis is presented and discussed. The program is written in the language of the Statistical Analysis System (SAS) but detailed knowledge of SAS is not required for its use. The program tests hypotheses about the goodness of fit of first- and second-order Markov models. It also tests if transition probabilities are homogeneous between the first and the second half of each sequence.Presented, in part, at the Association for the Advancement of Behavior Therapy Convention, November 1984.     

SPSS and SAS programs for addressing interdependence and basic levels-of-analysis issues in psychological data

Levels-of-analysis issues arise whenever individual-level data are collected from more than one person from the same dyad, family, classroom, work group, or other interaction unit. Interdependence in data from individuals in the same interaction units also violates the independence-of-observations assumption that underlies commonly used statistical tests. This article describes the data analysis challenges that are presented by these issues and presents SPSS and SAS programs for conducting appropriate analyses. The programs conduct the within- and-between-analyses described by Dansereau, Alutto, and Yammarino (1984) and the dyad-level analyses describedby Gonzalez and Griffin (1999) and Griffin and Gonzalez (1995). Contrasts with general multilevel modeling procedures are then discussed.     

SPSS and SAS programs for addressing interdependence and basic levels-of-analysis issues in psychological data.

Levels-of-analysis issues arise whenever individual-level data are collected from more than one person from the same dyad, family, classroom, work group, or other interaction unit. Interdependence in data from individuals in the same interaction units also violates the independence-of-observations assumption that underlies commonly used statistical tests. This article describes the data analysis challenges that are presented by these issues and presents SPSS and SAS programs for conducting appropriate analyses. The programs conduct the within-and-between-analyses described by Dansereau, Alutto, and Yammarino (1984) and the dyad-level analyses described by Gonzalez and Griffin (1999) and Griffin and Gonzalez (1995). Contrasts with general multilevel modeling procedures are then discussed.     

A loss function for alpha factor analysis

Most of the factor solutions can be got by minimizing a corresponding loss function. However, up to now, a loss function for the alpha factor analysis (AFA) has not been known. The present paper establishes such a loss function for the AFA. Some analogies to the maximum likelihood factor analysis are discussed.The author is greatly indebted to Prof. Henry F. Kaiser (University of California, Berkeley) for his kind encouragement. He is also indebted to an anonymous referee ofPsychometrika for having confronted him with the problem in 1977. Financial support by the Wiener Hochschuljubiläumsstiftung is gratefully acknowledged.     

A comparison of the LISREL and EQS programs for obtaining parameter estimates in confirmatory factor analysis studies

Recently, researchers in psychology have been provided with the techniques for confirming factor analytic structures. Many software packages are now available that provide the researcher with the ability to test factor structures and measurement models with some precision. However, the literature fails to provide the researcher with any comparison of the available software. This paper reviews the basic premise of confirmatory factor analysis and describes the use of two of the more popular software packages (e.g., LISREL and EQS) for obtaining parameter estimates. The two programs are then compared for similarity in estimates and ease of use.     

A note on the factor analysis of partial covariance matrices

A relationship is given between the joint common factor structure of two sets of variables, and the factor structure of the partial covariance matrix of one of the sets with the other partialled out.     

A comparison of the efficiency and accuracy of BILOG and LOGIST

Comparisons are made between BILOG version 2.2 and LOGIST 5.0 Version 2.5 in estimating the item parameters, traits, item characteristic functions (ICFs), and test characteristic functions (TCFs) for the three-parameter logistic model. Data analyzed are simulated item responses for 1000 simulees and one 10-item test, four 20-item tests, and four 40-item tests. LOGIST usually was faster than BILOG in producing maximum likelihood estimates. BILOG almost always produced more accurate estimates of individual item parameters. In estimating ICFs and TCFs BILOG was more accurate for the 10-item test, and the two programs were about equally accurate for the 20- and 40-item tests.I am grateful to Robert J. Mislevy, Martha L. Stocking, and Marilyn S. Wingersky for many helpful comments on an earlier version of this paper. I would also like to thank Hamid Kamrani and Bongmyoung Park for getting LOGIST and BILOG running and keeping them running under changing computer systems at CTB/McGraw-Hill.     

A feasible method for standard errors of estimate in maximum likelihood factor analysis

A jackknife-like procedure is developed for producing standard errors of estimate in maximum likelihood factor analysis. Unlike earlier methods based on information theory, the procedure developed is computationally feasible on larger problems. Unlike earlier methods based on the jackknife, the present procedure is not plagued by the factor alignment problem, the Heywood case problem, or the necessity to jackknife by groups. Standard errors may be produced for rotated and unrotated loading estimates using either orthogonal or oblique rotation as well as for estimates of unique factor variances and common factor correlations. The total cost for larger problems is a small multiple of the square of the number of variables times the number of observations used in the analysis. Examples are given to demonstrate the feasibility of the method.The research done by R. I. Jennrich was supported in part by NSF Grant MCS 77-02121. The research done by D. B. Clarkson was supported in part by NSERC Grant A3109.     

A second generation nonlinear factor analysis

Nonlinear common factor models with polynomial regression functions, including interaction terms, are fitted by simultaneously estimating the factor loadings and common factor scores, using maximum-likelihood-ratio and ordinary-least-squares methods. A Monte Carlo study gives support to a conjecture about the form of the distribution of the likelihood-ratio criterion.The research reported in this paper was partly supported by Natural Sciences and Engineering Research Grant No. A6346.     

A note on identification in the oblique and orthogonal factor analysis models

Conditions for removing the indeterminancy due to rotation are given for both the oblique and orthogonal factor analysis models. The conditions indicate why published counterexamples to conditions discussed by Jöreskog are not identifiable.The author would like to thank Gordon Bechtel and the reviewers for their comments and suggestions.     

Regression estimation and post-stratification in factor analysis

Regression estimation and poststratification are methods used in survey sampling to estimate a population mean, when additional information is available for some auxiliary variables. The extension of these methods to factor analysis is considered. These methods may be used either to improve the efficiency of estimation or to adjust for the effects of nonrandom selection. The estimation procedure may be formulated in a LISREL framework.The author is grateful to the referees for their comments.     

Loneliness and solitude in adolescence: A confirmatory factor analysis of alternative models

The present study tested a four-factor model of adolescent loneliness and solitude that comprises peer-related loneliness, family loneliness, negative attitude toward solitude, and positive attitude toward solitude. Nine different instruments for a total of 14 scales and derivative subscales were completed by a sample of mid-adolescents (N = 534) from Grades 10 through 12 (aged 15–18 years) in the Dutch-speaking part of Belgium. As expected, the four-factor solution provided a better fit to the data than did alternative models that comprised just a single factor, or two and three factors. Use of the Loneliness and Aloneness Scale for Children and Adolescents (LACA) is recommended, because the instrument measures all four aspects of the model. Implications for current theories on adolescent loneliness and associated phenomena, such as adolescents’ attitude toward being on their own, are briefly discussed.     

A bayesian estimation of factor score in confirmatory factor model with polytomous, censored or truncated data

The posterior analysis in estimating factor score in a confirmatory factor analysis model with polytomous, censored or truncated data is investigated in this paper. For the above three types of data, posterior distributions of the factor score are studied, and the estimators of the factor score are obtained to be the location parameters of the posterior distributions. The accuracy of Bayesian estimates is studied via simulation studies.This research was supported by a Hong Kong UGC grant.     

A new estimator of the uniqueness in factor analysis

A closed form estimator of the uniqueness (unique variance) in factor analysis is proposed. It has analytically desirable properties—consistency, asymptotic normality and scale invariance. The estimation procedure is given through the application to the two sets of Emmett's data and Holzinger and Swineford's data. The new estimator is shown to lead to values rather close to the maximum likelihood estimator.     

Statistical aspects of a three-mode factor analysis model

A special case of Bloxom's version of Tucker's three-mode model is developed statistically. A distinction is made between modes in terms of whether they are fixed or random. Parameter matrices are associated with the fixed modes, while no parameters are associated with the mode representing random observation vectors. The identification problem is discussed, and unknown parameters of the model are estimated by a weighted least squares method based upon a Gauss-Newton algorithm. A goodness-of-fit statistic is presented. An example based upon self-report and peer-report measures of personality shows that the model is applicable to real data. The model represents a generalization of Thurstonian factor analysis; weighted least squares estimators and maximum likelihood estimators of the factor model can be obtained using the proposed theory.This investigation was supported in part by a Research Scientist Development Award (K02-DA00017) and a research grant (DA01070) from the U. S. Public Health Service. The very helpful comments of several anonymous reviewers are gratefully acknowledged.     

Selection of variables in exploratory factor analysis: An empirical comparison of a stepwise and traditional approach

The purpose of this study was to investigate and compare the performance of a stepwise variable selection algorithm to traditional exploratory factor analysis. The Monte Carlo study included six factors in the design; the number of common factors; the number of variables explained by the common factors; the magnitude of factor loadings; the number of variables not explained by the common factors; the type of anomaly evidenced by the poorly explained variables; and sample size. The performance of the methods was evaluated in terms of selection and pattern accuracy, and bias and root mean squared error of the structure coefficients. Results indicate that the stepwise algorithm was generally ineffective at excluding anomalous variables from the factor model. The poor selection accuracy of the stepwise approach suggests that it should be avoided.     

Exploratory factor analysis in transportation research: Current practices and recommendations

Exploratory factor analysis (EFA) is a widely used statistical method in traffic and transportation research, particularly for the development and validation of measurement instruments. This article critically examines current practices in conducting and reporting EFA in published transportation studies. One hundred and eighty papers published between 2016 and 2018 were examined, of which eighty-two were included in the present study after applying eligibility criteria. The review suggests that the quality of EFA reported in the field is routinely poor: (a) researchers fail to provide sufficient information to be able to adequately assess the appropriateness and quality of both the input data and the reported output; and (b) the decisions underlying the choices of EFA methods are not justified and rely mostly on procedures advised against, particularly the Little-Jiffy approach. In summary, a significant gap between current practice and experts' recommendations exists. We provide some guidelines that may help in conducting, reporting and reviewing EFA in transportation research.     

A new algorithm for the least-squares solution in factor analysis

A new algorithm to obtain the least-squares or MINRES solution in common factor analysis is presented. It is based on the up-and-down Marquardt algorithm developed by the present authors for a general nonlinear least-squares problem. Experiments with some numerical models and some empirical data sets showed that the algorithm worked nicely and that SMC (Squared Multiple Correlation) performed best among four sets of initial values for common variances but that the solution might sometimes be very sensitive to fluctuations in the sample covariance matrix.Numerical computation was made on a NEAC S-1000 computer in the Computer Center, Osaka University.     

Exploratory longitudinal factor analysis in multiple populations

For multiple populatios, a longtidinal factor analytic model which is entirely exploratory, that is, no explicit identification constraints, is proposed. Factorial collapse and period/practice effects are allowed. An invariant and/or stationary factor pattern is permitted. This model is formulated stochastically. To implement this model a stagewise EM algorithm is developed. Finally a numerical illustration utilizing Nesselroade and Baltes' data is presented.The authors wish to thank Barbara Mellers and Henry Kaiser for their helpful comments and John Nesselroade for providing us the data for our illustration. This research wwa supported in part by a grant (No. AG03164) from the National Institute on Aging to William Meredith. Details of the derivations and a copy of the PROC MATRIX program are available upon request from the first author.     

The nonconvergence of factals: A nonmetric common factor analysis

FACTALS is a nonmetric common factor analysis model for multivariate data whose variables may be nominal, ordinal or interval. In FACTALS an Alternating Least Squares algorithm is utilized which is claimed to be monotonically convergent.In this paper it is shown that this algorithm is based upon an erroneous assumption, namely that the least squares loss function (which is in this case a nonscale free loss function) can be transformed into a scalefree loss function. A consequence of this is that monotonical convergence of the algorithm can not be guaranteed.