Configural Frequency Analysis: Methods, Models, and Applications

by von Eye; Alexander

• ISBN13: 9780805843231
• ISBN10: 080584323X
• Edition: 1st
• Format: Hardcover
• Copyright: 2002-06-01
• Publisher: Psychology Pres

Summary

Configural Frequency Analysis(CFA) provides an up-to-the-minute comprehensive introduction to its techniques, models, and applications. Written in a formal yet accessible style, actual empirical data examples are used to illustrate key concepts. Step-by-step program sequences are used to show readers how to employ CFA methods using commercial software packages, such as SAS, SPSS, SYSTAT, S-Plus, or those written specifically to perform CFA. CFA is an important method for analyzing results involved with categorical and longitudinal data. It allows one to answer the question of whether individual cells or groups of cells of cross-classifications differ significantly from expectations. The expectations are calculated using methods employed in log-linear modeling or a priori information. It is the only statistical method that allows one to make statements about empty areas in the data space. Applied and or person-oriented researchers, statisticians, and advanced students interested in CFA and categorical and longitudinal data will find this book to be a valuable resource. Developed since 1969, this method is now used by a large number of researchers around the world in a variety of disciplines, including psychology, education, medicine, and sociology. Configural Frequency Analysiswill serve as an excellent text for courses on configural frequency analysis, categorical variable analysis, or analysis of contingency tables. Prerequisites include an understanding of descriptive statistics, hypothesis testing, statistical model fitting, and some understanding of categorical data analysis and matrix algebra.

Table of Contents

Preface	ix
Part I: Concepts and Methods of CFA	1	(104)
Introduction: the Goals and Steps of Configural Frequency Analysis	1	(18)
Questions that can be answered with CFA	1	(4)
CFA and the Person Perspective	5	(3)
The five steps of CFA	8	(5)
A first complete CFA data example	13	(6)
Log-linear Base Models for CFA	19	(28)
Sample CFA base models and their design matrices	22	(5)
Admissibility of log-linear models as CFA base models	27	(4)
Sampling schemes and admissibility of CFA base models	31	(9)
Multinomial sampling	32	(1)
Product multinomial sampling	33	(1)
Sampling schemes and their implications for CFA	34	(6)
A grouping of CFA base models	40	(3)
The four steps of selecting a CFA base model	43	(4)
Statistical Testing in Global CFA	47	(50)
The null hypothesis in CFA	47	(1)
The binomial test	48	(6)
Three approximations of the binomial test	54	(4)
Approximation of the binomial test using Stirling's formula	54	(1)
Approximation of the binomial test using the DeMoivre-Laplace limit theorem	55	(1)
Standard normal approximation of the binomial test	56	(1)
Other approximations of the binomial test	57	(1)
The χ2 test and its normal approximation	58	(4)
Anscombe's normal approximation	62	(1)
Hypergeometric tests and approximations	62	(3)
Lehmacher's asymptotic hypergeometric test	63	(1)
Kuchenhoff's continuity correction for Lehmacher's test	64	(1)
Issues of power and the selection of CFA tests	65	(13)
Naud's power investigations	66	(3)
Applications of CFA tests	69	(1)
CFA of a sparse table	70	(6)
CFA in a table with large frequencies	76	(2)
Selecting significance tests for CFA	78	(3)
Finding types and antitypes: Issues of differential power	81	(4)
Methods of protecting α	85	(12)
The Bonferroni α protection (SS)	87	(1)
Holm's procedure for α protection (SD)	88	(1)
Hochberg's procedure for α protection (SU)	89	(1)
Holland and Copenhaver's procedure for α protection	90	(1)
Hommel, Lehmacher, and Perli's modifications of Holm's procedure for protection of the multiple level α (SD)	90	(2)
Illustrating the procedures for protecting the test-wise α	92	(5)
Descriptive Measures for Global CFA	97	(8)
The relative risk ratio, RR	97	(1)
The measure log P	98	(1)
Comparing the X2 component with the relative risk ratio and log P	99	(6)
Part II: Models and Applications of CFA	105	(98)
Global Models of CFA	105	(20)
Zero order global CFA	106	(4)
First order global CFA	110	(8)
Data example I: First order CFA of social network data	111	(4)
Data example II: First order CFA of Finkelstein's Tanner data, Waves 2 and 3	115	(3)
Second order global CFA	118	(3)
Third order global CFA	121	(4)
Regional Models of CFA	125	(48)
Interaction Structure Analysis (ISA)	125	(14)
ISA of two groups of variables	126	(9)
ISA of three or more groups of variables	135	(4)
Prediction CFA	139	(34)
Base models for Prediction CFA	139	(13)
More P-CFA models and approaches	152	(1)
Conditional P-CFA: Stratifying on a variable	152	(7)
Biprediction CFA	159	(5)
Prediction coefficients	164	(9)
Comparing k Samples	173	(30)
Two-sample CFA I: The original approach	173	(5)
Two-sample CFA II: Alternative methods	178	(12)
Gonzales-Deben's π*	179	(1)
Goodman's three elementary views of non-independence	180	(6)
Measuring effect strength in two-sample CFA	186	(4)
Comparing three or more samples	190	(5)
Three groups of variables: ISA plus k-sample CFA	195	(8)
Part III: Methods of Longitudinal CFA	203	(76)
CFA of Differences	205	(24)
A review of methods of differences	206	(6)
The method of differences in CFA	212	(17)
Depicting the shape of curves by differences: An example	213	(1)
Transformations and the size of the table under study	214	(2)
Estimating expected cell frequencies for CFA of differences	216	(1)
Calculating a priori probabilities: Three examples	216	(4)
Three data examples	220	(7)
CFA of second differences	227	(2)
CFA of Level, Variability, and Shape of Series of Observations	229	(50)
CFA of shifts in location	229	(7)
CFA of variability in a series of measures	236	(4)
Considering both level and trend in the analysis of series of measures	240	(16)
Estimation and CFA of polynomial parameters for equidistant points on X	241	(3)
Orthogonal polynomials	244	(4)
Configural analysis of polynomial coefficients	248	(3)
Estimation and CFA of polynomial parameters for non-equidistant points on X	251	(5)
CFA of series that differ in length; an example of confirmatory CFA	256	(3)
Examining treatment effects using CFA; more confirmatory CFA	259	(6)
Treatment effects in pre-post designs (no control group)	259	(4)
Treatment effects in control group designs	263	(2)
CFA of patterns of correlation or multivariate distance sequences	265	(6)
CFA of autocorrelations	266	(3)
CFA of autodistances	269	(2)
Unidimensional CFA	271	(3)
Within-individual CFA	274	(5)
Part IV: The CFA Specialty File and Alternative Approaches to CFA	279	(82)
More Facets of CFA	280	(67)
CFA of cross-classifications with structural zeros	280	(4)
The parsimony of CFA base models	284	(9)
CFA of groups of cells: Searching for patterns of types and antitypes	293	(2)
CFA and the exploration of causality	295	(14)
Exploring the concept of the wedge using CFA	296	(5)
Exploring the concept of the fork using CFA	301	(4)
Exploring the concept of reciprocal causation using CFA	305	(4)
Covariates in CFA	309	(14)
Categorical covariates: stratification variables	309	(7)
Continuous covariates	316	(7)
CFA of ordinal variables	323	(3)
Graphical displays of CFA results	326	(8)
Displaying the patterns of types and antitypes based on test statistics or frequencies	327	(3)
Mosaic displays	330	(4)
Aggregating results from CFA	334	(4)
Employing CFA in tandem with other methods of analysis	338	(9)
CFA and cluster analysis	338	(4)
CFA and discriminant analysis	342	(5)
Alternative Approaches to CFA	347	(14)
Kieser and Victor's quasi-independence model of CFA	347	(6)
Bayesian CFA	353	(8)
The prior and posterior distributions	354	(2)
Types and antitypes in Bayesian CFA	356	(1)
Patterns of types and antitypes and protecting α	356	(1)
Data examples	357	(4)
Part V: Computational Issues	361	(40)
Software to Perform CFA	361	(40)
Using SYSTAT to perform CFA	362	(9)
SYSTAT's two-way cross-tabulation module	362	(5)
SYSTAT's log-linear modeling module	367	(4)
Using S-plus to perform Bayesian CFA	371	(3)
Using CFA 2002 to perform Frequentist CFA	374	(27)
Program description	375	(4)
Sample applications	379	(1)
First order CFA; keyboard input of frequency table	379	(5)
Two-sample CFA with two predictors; keyboard input	384	(6)
Second Order CFA; data input via file	390	(4)
CFA with covariates; input via file (Frequencies) and keyboard (covariate)	394	(7)
Part VI: References, Appendices, and Indices	401	(1)
References	401	(22)
Appendix A: A brief introduction to log-linear modeling	423	(10)
Appendix B: Table of α*-levels for the Bonferroni and Holm adjustments	433	(6)
Author Index	439	(6)
Subject Index	445