*Christine DeMars*

- Published in print:
- 2010
- Published Online:
- March 2012
- ISBN:
- 9780195377033
- eISBN:
- 9780199847341
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195377033.003.0003
- Subject:
- Psychology, Cognitive Psychology

This chapter offers an in-depth discussion of the three statistical assumptions of item response theory (IRT), namely unidimensionality, local independence, and correct model specification. Each of ...
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This chapter offers an in-depth discussion of the three statistical assumptions of item response theory (IRT), namely unidimensionality, local independence, and correct model specification. Each of these assumptions is described more fully, with a focus on procedures for testing each assumption. For each assumption, a number of statistical tests is proposed and explored in the literature. In addition, three common methods for testing unidimensionality are discussed: analysis of the eigenvalues of the inter-item correlation matrix, Stout's test of essential unidimensionality, and indices based on the residuals from a unidimensional solution. Weaknesses of some common approaches and indices is noted, and newer alternative procedures are described. Unfortunately, some of these procedures are quite complex and not easily implemented.Less

This chapter offers an in-depth discussion of the three statistical assumptions of item response theory (IRT), namely unidimensionality, local independence, and correct model specification. Each of these assumptions is described more fully, with a focus on procedures for testing each assumption. For each assumption, a number of statistical tests is proposed and explored in the literature. In addition, three common methods for testing unidimensionality are discussed: analysis of the eigenvalues of the inter-item correlation matrix, Stout's test of essential unidimensionality, and indices based on the residuals from a unidimensional solution. Weaknesses of some common approaches and indices is noted, and newer alternative procedures are described. Unfortunately, some of these procedures are quite complex and not easily implemented.

*Patrick Dattalo*

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199773596
- eISBN:
- 9780199332564
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199773596.001.0001
- Subject:
- Social Work, Research and Evaluation

Multivariate procedures allow social workers and other human services researchers to analyze complex, multidimensional social problems and interventions in ways that minimize oversimplification. This ...
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Multivariate procedures allow social workers and other human services researchers to analyze complex, multidimensional social problems and interventions in ways that minimize oversimplification. This book provides an introduction to four procedures for the analysis of multiple dependent variables: multivariate analysis of variance (MANOVA), multivariate analysis of covariance (MANCOVA), multivariate multiple regression (MMR), and structural equation modeling (SEM). Each procedure is presented in a way that allows readers to compare and contrast them in terms of appropriate research context; required statistical assumptions, including levels of measurement of variables to be modeled; analytical steps; sample size; and strengths and weaknesses. This book facilitates course extensibility in scope and depth by allowing instructors to supplement course content with rigorous statistical procedures. The book provides detailed annotated examples using Stata, SPSS (PASW), SAS, and Amos.Less

Multivariate procedures allow social workers and other human services researchers to analyze complex, multidimensional social problems and interventions in ways that minimize oversimplification. This book provides an introduction to four procedures for the analysis of multiple dependent variables: multivariate analysis of variance (MANOVA), multivariate analysis of covariance (MANCOVA), multivariate multiple regression (MMR), and structural equation modeling (SEM). Each procedure is presented in a way that allows readers to compare and contrast them in terms of appropriate research context; required statistical assumptions, including levels of measurement of variables to be modeled; analytical steps; sample size; and strengths and weaknesses. This book facilitates course extensibility in scope and depth by allowing instructors to supplement course content with rigorous statistical procedures. The book provides detailed annotated examples using Stata, SPSS (PASW), SAS, and Amos.

*Karen A. Randolph and Laura L. Myers*

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199764044
- eISBN:
- 9780199332533
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199764044.003.0001
- Subject:
- Social Work, Research and Evaluation

Chapter 1 defines important terms including basic statistics, multivariate analysis, and inferential statistics, as a way to introduce readers to the book’s premise—that a thorough understanding of ...
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Chapter 1 defines important terms including basic statistics, multivariate analysis, and inferential statistics, as a way to introduce readers to the book’s premise—that a thorough understanding of basic statistics is critical in the successful application of more advanced statistical methods. Readers are also introduced to assumptions and other requirements necessary for inferential statistical testing, making predictions about relationships between variables, and making causal inferences. The chapter then provides a description of each of the multivariate methods—multiple linear regression, Analysis of variance and Covariance, and path analysis—covered in the book. The chapter concludes with an overview of subsequent chapters and a description of the National Educational Longitudinal Study of 1988 (NELS: 88), which is the data set used for the book’s examples of each method.Less

Chapter 1 defines important terms including basic statistics, multivariate analysis, and inferential statistics, as a way to introduce readers to the book’s premise—that a thorough understanding of basic statistics is critical in the successful application of more advanced statistical methods. Readers are also introduced to assumptions and other requirements necessary for inferential statistical testing, making predictions about relationships between variables, and making causal inferences. The chapter then provides a description of each of the multivariate methods—multiple linear regression, Analysis of variance and Covariance, and path analysis—covered in the book. The chapter concludes with an overview of subsequent chapters and a description of the National Educational Longitudinal Study of 1988 (NELS: 88), which is the data set used for the book’s examples of each method.

*M. D. Edge*

- Published in print:
- 2019
- Published Online:
- October 2019
- ISBN:
- 9780198827627
- eISBN:
- 9780191866463
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198827627.003.0013
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

Becoming a well-rounded data analyst requires more than the skills covered in this book. This postlude sketches some ways in which the types of thinking covered here can be extended to real problems ...
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Becoming a well-rounded data analyst requires more than the skills covered in this book. This postlude sketches some ways in which the types of thinking covered here can be extended to real problems in data analysis. Different ways of evaluating the assumptions of linear regression are considered, including plotting, hypothesis tests, and out-of-sample prediction. If the assumptions are not met, simple linear regression can be extended in various ways, including multiple regression, generalized linear models, and mixed models (among many other possibilities). This postlude concludes with a short discussion of the themes of the book: probabilistic models, methodological pluralism, and the value of elementary statistical thinking.Less

Becoming a well-rounded data analyst requires more than the skills covered in this book. This postlude sketches some ways in which the types of thinking covered here can be extended to real problems in data analysis. Different ways of evaluating the assumptions of linear regression are considered, including plotting, hypothesis tests, and out-of-sample prediction. If the assumptions are not met, simple linear regression can be extended in various ways, including multiple regression, generalized linear models, and mixed models (among many other possibilities). This postlude concludes with a short discussion of the themes of the book: probabilistic models, methodological pluralism, and the value of elementary statistical thinking.