Michael W Browne
Biographic Data
| ID | 333806 |
|---|---|
| NAME | Michael W Browne |
| GIVEN NAMES | Michael W |
| FAMILY NAME | Browne |
| SIGNATURE | BROWNE M W |
| AFFILIATIONS | The Ohio State University |
| VERIFIED | No |
| TOTAL WORKS | 17 |
| TOTAL CITATIONS | 1800 |
| AUTHOR COUNT | 17 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1982 |
| LATEST PUBLICATION YEAR | 2011 |
| H-INDEX | 2 |
Higher-Order Factor Invariance and Idiographic Mapping of Constructs to Observables
Theory, research, and application in developmental science share the conceptual and methodological challenges of integrating the study of the course of a person's intra-individual changes and the formulation of subgroup (differential) or nomothetic generalizations. One approach to these challenges has involved building tailored construct representations that filter out irrelevant idiosyncratic information hampering the articulation of nomothetic …
Bootstrap Standard Error Estimates in Dynamic Factor Analysis
Dynamic factor analysis summarizes changes in scores on a battery of manifest variables over repeated measurements in terms of a time series in a substantially smaller number of latent factors. Algebraic formulae for standard errors of parameter estimates are more difficult to obtain than in the usual intersubject factor analysis because of the interdependence of successive observations. Bootstrap methods can fill this need, however. The standard…
Structural Equation Modeling of Multivariate Time Series
The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be employed to fit the model. Particular attention is given to assumptions concerning the process before …
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 al…
How Can I Connect With Thee?: Let Me Count the Ways
Two studies were conducted to examine mental representations of loneliness and social connectedness. In Study 1, young adults (N = 2,531) completed the revised UCLA Loneliness Scale (R-UCLA scale) and demographic questionnaires. An exploratory factor analysis of the R-UCLA scale on half the sample revealed a three-dimensional conceptual structure that generalized across gender. This mental representation consisted of correlated facets labeled Iso…
An Overview of Analytic Rotation in Exploratory Factor Analysis
The use of analytic rotation in exploratory factor analysis will be examined. Particular attention will be given to situations where there is a complex factor pattern and standard methods yield poor solutions. Some little known but interesting rotation criteria will be discussed and methods for weighting variables will be examined. Illustrations will be provided using Thurstone's 26 variable box data and other examples
Power analysis and determination of sample size for covariance structure modeling.
A framework for hypothesis testing and power analysis in the assessment of fit of covariance structure models is presented. We emphasize the value of confidence intervals for fit indices, and we stress the relationship of confidence intervals to a framework for hypothesis testing. The approach allows for testing null hypotheses of not-good fit, reversing the role of the null hypothesis in conventional tests of model fit, so that a significant res…
The use of causal indicators in covariance structure models: Some practical issues
The use of causal indicators in covariance structure models: Some practical issues
In conventional representations of covariance structure models, indicators are defined as linear functions of latent variables, plus error. In an alternative representation, constructs can be defined as linear functions of their indicators, called causal indicators, plus an error term. Such constructs are not latent variables but composite variables, and they have no indicators in the conventional sense. The presence of composite variables in a m…
Circumplex Models for Correlation Matrices
Structural models that yield circumplex inequality patterns for the elements of correlation matrices are reviewed. Particular attention is given to a stochastic process defined on the circle proposed by T. W. Anderson. It is shown that the Anderson circumplex contains the Markov Process model for a simplex as a limiting case when a parameter tends to infinity. Anderson's model is intended for correlation matrices with positive elements. A replace…
Automated Fitting of Nonstandard Models
A method for automated parameter estimation and testing of fit of nonstandard models for mean vectors and covariance matrices is described. Nonlinear equality and inequality constraints on the parameters of the model are allowed for. All the user will need to provide are subroutines to evaluate the mean vector and covariance matrix according to the model and, if required, the constraint functions. Subroutines for derivatives need not be provided.…
Alternative Ways of Assessing Model Fit
This article is concerned with measures of fit of a model. Two types of error involved in fitting a model are considered. The first is error of approximation which involves the fit of the model, with optimally chosen but unknown parameter values, to the population covariance matrix. The second is overall error which involves the fit of the model, with parameter values estimated from the sample, to the population covariance matrix. Measures of the…
Single Sample Cross-Validation Indices for Covariance Structures
This article considers single sample approximations for the cross-validation coefficient in the analysis of covariance structures. An adjustment for predictive validity which may be employed in conjunction with any correctly specified discrepancy function is suggested. In the case of maximum likelihood estimation under normality assumptions the coefficient obtained is a simple linear function of the Akaike Information Criterion. Results of a rand…
On the Multivariate Asymptotic Distribution of Sequential Chi-Square Statistics
The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-square difference tests are asymptotically independent. Some Monte Carlo evidence on t…
Asymptotically distribution‐free methods for the analysis of covariance structures
Methods for obtaining tests of fit of structural models for covariance matrices and estimator standard errors which are asymptotically distribution free are derived. Modifications to standard normal theory tests and standard errors which make them applicable to the wider class of elliptical distributions are provided. A random sampling experiment to investigate some of the proposed methods is described.
Cross-Validation Of Covariance Structures
This paper examines methods for comparing the suitability of alternative models for covariance matrices. A cross-validation procedure is suggested and its properties are examined. To motivate the discussion, a series of examples is presented using longitudinal data
Covariance Structures
INTRODUCTION Structural models for covariance matrices are used when studying relationships between variables and are employed predominantly in the social sciences. The best known of these is the factor analysis model but recently there has been rapid development of extensions and alternatives. Most of this work has appeared in psychometric journals. Textbooks on applied multivariate analysis are recently including chapters on factor analysis. Th…
Alternative Ways of Assessing Model Fit
This article is concerned with measures of fit of a model. Two types of error involved in fitting a model are considered. The first is error of approximation which involves the fit of the model, with optimally chosen but unknown parameter values, to the population covariance matrix. The second is overall error which involves the fit of the model, with parameter values estimated from the sample, to the population covariance matrix. Measures of the…
The use of causal indicators in covariance structure models: Some practical issues
In conventional representations of covariance structure models, indicators are defined as linear functions of latent variables, plus error. In an alternative representation, constructs can be defined as linear functions of their indicators, called causal indicators, plus an error term. Such constructs are not latent variables but composite variables, and they have no indicators in the conventional sense. The presence of composite variables in a m…
Covariance Structures
INTRODUCTION Structural models for covariance matrices are used when studying relationships between variables and are employed predominantly in the social sciences. The best known of these is the factor analysis model but recently there has been rapid development of extensions and alternatives. Most of this work has appeared in psychometric journals. Textbooks on applied multivariate analysis are recently including chapters on factor analysis. Th…
Cross-Validation Of Covariance Structures
This paper examines methods for comparing the suitability of alternative models for covariance matrices. A cross-validation procedure is suggested and its properties are examined. To motivate the discussion, a series of examples is presented using longitudinal data
Asymptotically distribution‐free methods for the analysis of covariance structures
Methods for obtaining tests of fit of structural models for covariance matrices and estimator standard errors which are asymptotically distribution free are derived. Modifications to standard normal theory tests and standard errors which make them applicable to the wider class of elliptical distributions are provided. A random sampling experiment to investigate some of the proposed methods is described.
On the Multivariate Asymptotic Distribution of Sequential Chi-Square Statistics
The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-square difference tests are asymptotically independent. Some Monte Carlo evidence on t…
Single Sample Cross-Validation Indices for Covariance Structures
This article considers single sample approximations for the cross-validation coefficient in the analysis of covariance structures. An adjustment for predictive validity which may be employed in conjunction with any correctly specified discrepancy function is suggested. In the case of maximum likelihood estimation under normality assumptions the coefficient obtained is a simple linear function of the Akaike Information Criterion. Results of a rand…
Circumplex Models for Correlation Matrices
Structural models that yield circumplex inequality patterns for the elements of correlation matrices are reviewed. Particular attention is given to a stochastic process defined on the circle proposed by T. W. Anderson. It is shown that the Anderson circumplex contains the Markov Process model for a simplex as a limiting case when a parameter tends to infinity. Anderson's model is intended for correlation matrices with positive elements. A replace…
Automated Fitting of Nonstandard Models
A method for automated parameter estimation and testing of fit of nonstandard models for mean vectors and covariance matrices is described. Nonlinear equality and inequality constraints on the parameters of the model are allowed for. All the user will need to provide are subroutines to evaluate the mean vector and covariance matrix according to the model and, if required, the constraint functions. Subroutines for derivatives need not be provided.…
Alternative Ways of Assessing Model Fit
This article is concerned with measures of fit of a model. Two types of error involved in fitting a model are considered. The first is error of approximation which involves the fit of the model, with optimally chosen but unknown parameter values, to the population covariance matrix. The second is overall error which involves the fit of the model, with parameter values estimated from the sample, to the population covariance matrix. Measures of the…
The use of causal indicators in covariance structure models: Some practical issues
The use of causal indicators in covariance structure models: Some practical issues
In conventional representations of covariance structure models, indicators are defined as linear functions of latent variables, plus error. In an alternative representation, constructs can be defined as linear functions of their indicators, called causal indicators, plus an error term. Such constructs are not latent variables but composite variables, and they have no indicators in the conventional sense. The presence of composite variables in a m…
Power analysis and determination of sample size for covariance structure modeling.
A framework for hypothesis testing and power analysis in the assessment of fit of covariance structure models is presented. We emphasize the value of confidence intervals for fit indices, and we stress the relationship of confidence intervals to a framework for hypothesis testing. The approach allows for testing null hypotheses of not-good fit, reversing the role of the null hypothesis in conventional tests of model fit, so that a significant res…
An Overview of Analytic Rotation in Exploratory Factor Analysis
The use of analytic rotation in exploratory factor analysis will be examined. Particular attention will be given to situations where there is a complex factor pattern and standard methods yield poor solutions. Some little known but interesting rotation criteria will be discussed and methods for weighting variables will be examined. Illustrations will be provided using Thurstone's 26 variable box data and other examples
How Can I Connect With Thee?: Let Me Count the Ways
Two studies were conducted to examine mental representations of loneliness and social connectedness. In Study 1, young adults (N = 2,531) completed the revised UCLA Loneliness Scale (R-UCLA scale) and demographic questionnaires. An exploratory factor analysis of the R-UCLA scale on half the sample revealed a three-dimensional conceptual structure that generalized across gender. This mental representation consisted of correlated facets labeled Iso…
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 al…
Structural Equation Modeling of Multivariate Time Series
The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be employed to fit the model. Particular attention is given to assumptions concerning the process before …
Bootstrap Standard Error Estimates in Dynamic Factor Analysis
Dynamic factor analysis summarizes changes in scores on a battery of manifest variables over repeated measurements in terms of a time series in a substantially smaller number of latent factors. Algebraic formulae for standard errors of parameter estimates are more difficult to obtain than in the usual intersubject factor analysis because of the interdependence of successive observations. Bootstrap methods can fill this need, however. The standard…
Higher-Order Factor Invariance and Idiographic Mapping of Constructs to Observables
Theory, research, and application in developmental science share the conceptual and methodological challenges of integrating the study of the course of a person's intra-individual changes and the formulation of subgroup (differential) or nomothetic generalizations. One approach to these challenges has involved building tailored construct representations that filter out irrelevant idiosyncratic information hampering the articulation of nomothetic …
Mathematics (16 works) · Statistics (16 works) · Covariance (11 works) · Econometrics (10 works) · Computer Science (8 works) · Advanced Statistical Methods and Models (7 works) · Applied Mathematics (6 works) · Analysis of covariance (4 works) · Covariance matrix (4 works) · Psychometric Methodologies and Testing (4 works)