EPSY 5245 EPSY 5245 Michael C. Rodriguez

Slides:



Advertisements
Similar presentations
IEA Teacher Education Study in Mathematics 3 rd NRC Meeting, June 25-29, Taipei, Chinese Taipei. Michael C. Rodriguez University of Minnesota & Michigan.
Advertisements

Aaker, Kumar, Day Seventh Edition Instructor’s Presentation Slides
1 COMM 301: Empirical Research in Communication Kwan M Lee Lect4_1.
Some (Simplified) Steps for Creating a Personality Questionnaire Generate an item pool Administer the items to a sample of people Assess the uni-dimensionality.
Chapter Nineteen Factor Analysis.
Lecture 7: Principal component analysis (PCA)
Psychology 202b Advanced Psychological Statistics, II April 7, 2011.
© 2005 The McGraw-Hill Companies, Inc., All Rights Reserved. Chapter 14 Using Multivariate Design and Analysis.
Factor Analysis Ulf H. Olsson Professor of Statistics.
Principal Components An Introduction Exploratory factoring Meaning & application of “principal components” Basic steps in a PC analysis PC extraction process.
Common Factor Analysis “World View” of PC vs. CF Choosing between PC and CF PAF -- most common kind of CF Communality & Communality Estimation Common Factor.
When Measurement Models and Factor Models Conflict: Maximizing Internal Consistency James M. Graham, Ph.D. Western Washington University ABSTRACT: The.
Item Response Theory. Shortcomings of Classical True Score Model Sample dependence Limitation to the specific test situation. Dependence on the parallel.
GRA 6020 Multivariate Statistics Factor Analysis Ulf H. Olsson Professor of Statistics.
Factor Analysis Ulf H. Olsson Professor of Statistics.
Measurement Models and CFA Ulf H. Olsson Professor of Statistics.
Education 795 Class Notes Factor Analysis II Note set 7.
Chapter 7 Correlational Research Gay, Mills, and Airasian
Multivariate Methods EPSY 5245 Michael C. Rodriguez.
Factor Analysis Psy 524 Ainsworth.
Principal Components An Introduction
Social Science Research Design and Statistics, 2/e Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton Factor Analysis PowerPoint Prepared by Alfred.
MEASUREMENT MODELS. BASIC EQUATION x =  + e x = observed score  = true (latent) score: represents the score that would be obtained over many independent.
Measuring the Unobservable
MGMT 6971 PSYCHOMETRICS © 2014, Michael Kalsher
Advanced Correlational Analyses D/RS 1013 Factor Analysis.
Applied Quantitative Analysis and Practices
Measurement Models: Exploratory and Confirmatory Factor Analysis James G. Anderson, Ph.D. Purdue University.
Introduction to Multivariate Analysis of Variance, Factor Analysis, and Logistic Regression Rubab G. ARIM, MA University of British Columbia December 2006.
Marketing Research Aaker, Kumar, Day and Leone Tenth Edition Instructor’s Presentation Slides 1.
CFA: Basics Beaujean Chapter 3. Other readings Kline 9 – a good reference, but lumps this entire section into one chapter.
© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 1 Chapter 12 Testing for Relationships Tests of linear relationships –Correlation 2 continuous.
Lecture 12 Factor Analysis.
Multivariate Analysis and Data Reduction. Multivariate Analysis Multivariate analysis tries to find patterns and relationships among multiple dependent.
Applied Quantitative Analysis and Practices
Education 795 Class Notes Factor Analysis Note set 6.
Exploratory Factor Analysis Principal Component Analysis Chapter 17.
Chapter 13.  Both Principle components analysis (PCA) and Exploratory factor analysis (EFA) are used to understand the underlying patterns in the data.
Department of Cognitive Science Michael Kalsher Adv. Experimental Methods & Statistics PSYC 4310 / COGS 6310 Factor Analysis 1 PSYC 4310 Advanced Experimental.
Factor Analysis I Principle Components Analysis. “Data Reduction” Purpose of factor analysis is to determine a minimum number of “factors” or components.
Advanced Statistics Factor Analysis, I. Introduction Factor analysis is a statistical technique about the relation between: (a)observed variables (X i.
Applied Quantitative Analysis and Practices LECTURE#19 By Dr. Osman Sadiq Paracha.
FACTOR ANALYSIS 1. What is Factor Analysis (FA)? Method of data reduction o take many variables and explain them with a few “factors” or “components”
Principal Component Analysis
FACTOR ANALYSIS.  The basic objective of Factor Analysis is data reduction or structure detection.  The purpose of data reduction is to remove redundant.
Chapter 14 EXPLORATORY FACTOR ANALYSIS. Exploratory Factor Analysis  Statistical technique for dealing with multiple variables  Many variables are reduced.
Methods of multivariate analysis Ing. Jozef Palkovič, PhD.
FACTOR ANALYSIS & SPSS.
Exploratory Factor Analysis
Principal Components & Common Factoring An Introduction
EXPLORATORY FACTOR ANALYSIS (EFA)
Analysis of Survey Results
Evaluation of measuring tools: validity
assessing scale reliability
12 Inferential Analysis.
Measuring latent variables
Reliability and Validity of Measurement
Dr. Chin and Dr. Nettelhorst Winter 2018
Measuring latent variables
An Introduction to Factor Analysis
Measuring latent variables
12 Inferential Analysis.
Principal Component Analysis
Chapter_19 Factor Analysis
Chapter 6 Predicting Future Performance
Lecture 8: Factor analysis (FA)
Measuring latent variables
Presentation transcript:

EPSY 5245 EPSY 5245 Michael C. Rodriguez Multivariate Methods EPSY 5245 Michael C. Rodriguez

Cluster Analysis Generic name for a variety of procedures. The procedures form clusters of similar entities (usually persons, but can be variables). Groups persons based on commonalities on several variables. Cases within a cluster are more alike than cases between clusters. Definition of the variables on which to cluster is critical, as this defines the characteristic of each cluster.

Clustering for what? Development of a classification or typology. Investigate useful conceptual frameworks for grouping entities. A method of data reduction to manage large samples.

Statistical Framework No statistical basis – no ability to draw statistical inferences regarding results. Exploratory technique. Solutions are not unique – slight variation in procedures can create different clusters. The procedure ALWAYS creates clusters, even if they DO NOT really exist in the population.

Methods of Clustering Hierarchical: cases are joined in a cluster and they remain in that cluster as other clusters are formed. Non-Hierarchical: cases can switch clusters as the cluster formation proceeds (not discussed further here).

Hierarchical Clustering This procedure attempts to identify relatively homogeneous groups of cases based on selected characteristics, using an algorithm that starts with each case in a separate cluster and combines clusters until only one is left. Source: SPSS (Help Menu)

Hierarchical Clustering The variables can be continuous, dichotomous, or count data. Scaling of variables is an important issue, as differences in scaling may affect your cluster solution(s). For example, one variable is measured in dollars and the other is measured in years. You should consider standardizing them. Can be done automatically by the Hierarchical Cluster Analysis procedure. Source: SPSS (Help Menu)

Using Cluster Analysis Identify the important characteristics to define the clusters. Select the method of clustering. Check the number of cases in each cluster (very small clusters are not useful). Assess whether clusters make sense. Validate the clusters by examining how they relate to other important variables. Source: SPSS (2003)

Cluster Examples Archeological Data

Reliability Analysis Reliability Analysis examines the consistency of the total score and contribution of each item to the total score. Coefficient Alpha Coefficient Omega Generalizability Theory Item-Total Correlations

Coefficient Alpha Coefficient Alpha is an index of score reliability. Technically speaking, it is the proportion of observed variance that is true (systematic) variance. It tells us degree to which scores are reliable, consistent, replicable. This should be above .70 for research purposes (when above .90, scores for individuals can be used). Alpha is not an index of unidimensionality, but may indicate the presence of a “common factor”.

Item-Total Correlations Total score is based on the sum of items – but not necessarily a unidimensional measure. Commonly referred to as item discrimination; does the item discriminate between people high or low on the trait. Does the item contribute to the total score (total measure)? Should be positive and relatively high (.30+).

Corrected Item-Total Correlation EPSY 5245 Reliability Statistics Cronbach's Alpha N of Items .364 5 Corrected Item-Total Correlation Like mathematics .502 Enjoy learning math .543 Math is boring -.584 Math is an easy subject .445 Like a job involving math .459

Corrected Item-Total Correlation Reliability Statistics Cronbach's Alpha N of Items .790 4 Corrected Item-Total Correlation Like mathematics .690 Enjoy learning math .706 Math is an easy subject .468 Like a job involving math .557

Reliability Examples TIMSS Data

Factor Analysis Factor Analysis examines the inter-correlations of items, identifies items that are correlated as sets. Factor Loadings Variance Explained Polychoric correlations Two ordinal variables

Factor Loadings A factor is a unidimensional measure of “something”. A loading is a correlation between the item and factor. Does the item contribute to the total factor? Should be positive and relatively high (.50+).

Variance Explained Each item contributes variance. The total variance is the sum of the item variances. As a set, the factor accounts for variance from all the items. If the factor is an efficient summary of all of the items, it will explain a large percent of the total variance. % Variance Explained 47.9

Factor Scores Factor scores can be used in analysis – based on the factor analysis results. A factor score is a single score resulting from the weighted combination of item scores. The weights are based on the factor loadings. These scores retain the percent of variance accounted for by the factor.

EFA Exploratory factor analysis allows all items to load on each factor. Explores the underlying factor structure. No test for fit or whether the factor structure is the best solution – it is simply one solution.

CFA Confirmatory factor analysis requires a priori specification of factors. Provides a test of fit between the factor structure and the data. Allows for comparisons of the factor structure fit across groups.

CFI = .996 NFI = .987 RMSEA = .078

Specifying Factors Variables are standardized (SD = 1, Var = 1). Total variance is equal to the number of items. The Eigenvalue is the amount of variance accounted for by each factor. Eigenvalues > 1.0 are efficient summaries of items; worth more than a single item. A scree plot helps identify number of efficient factors.

Extraction Method Principal Components Analysis: Assumes no measurement error and all items are weighted equally – NOT true EFA. Principal Axis Factoring: Employs communalities (i.e., explained variance) to facilitate the identification of the factor structure – traditional EFA. With large samples, most methods yield similar results.

Principal Components Analysis A data reduction technique – reducing a large number of variables into efficient components Principal components are linear combinations of the measures and contain common and unique variance EFA decomposes variance into the part due to common factors and that due to unique factors

Rotation Rotation helps identify the simple structure. Maximizes differences between the high and low loadings or maximizes the variance between factors. Orthogonal rotation requires that the resulting factors are uncorrelated. Oblique rotation allows factors to be correlated.

Practical Issues Need at least 10 cases per variable or per question in the model. CFA requires more cases – at least 200 for a standard model. Should have measurements from at least 3 variables for each factor you hope to include. In EFA, you should try to write items that span the range of possible items for each potential factor (construct).

Using Factors A factor is not very useful for research purposes if it is not sensitive to group differences. Factors should be both theoretically defensible and empirically defensible.

Factor Analysis Examples Aggression Data

Multivariate Structure Cluster analysis is primarily concerned with grouping cases (persons). Creating subgroups Factor analysis is primarily concerned with grouping variables. Creating measures Assessing structure is the common characteristic between these two methods.

Grimm, L. G. & Yarnold, P. R. (Eds. ). (2000) Grimm, L.G. & Yarnold, P.R. (Eds.). (2000). Reading and understanding more multivariate statistics. Washington DC: American Psychological Association.