Configural frequency analysis methods, models and applications

List of contents Preface Part I: Concepts and Methods of CFA ix 1 Introduction: the Goals and Steps of Configural Frequency Analysis 1.1 Questionsthat can be answeredwith CFA 1.2 CFA and the PersonPerspective 1.3 The five stepsof CFA 1.4 A first completeCFA data example 13 Log-linear Base Models for CFA 19 2.1 SampleCFA basemodels and their designmatrices 22 2.2 Admissibility of log-linear models as CFA base models 27 2.3 Sampling schemesand admissibility of CFA base models 31 2.3.1 Multinomial sampling 32 2.3.2 Product multinomial sampling 33 2.3.3 Sampling schemesand their implications for CFA 34 2.4 A grouping of CFA basemodels 40 2.5 The four stepsof selectinga CFA basemodel 43 Statistical Testing in Global CFA 47 3.1 The null hypothesisin CFA 47 3.2 The binomial test 48 3.3 Three approximationsof the binomial test 54 List of Contents 3.3.1 Approximation of the binomial test using Stirling’s formula 54 3.3.2 Approximation of the binomial test using the DeMoivre-Laplace limit theorem 55 3.3.3 Standardnormal approximation of the binomial test 56 3.3.4 Other approximationsof the binomial test 57 3.4 The test and its normal approximation 58 3.5 Anscombe’snormal approximation 62 3.6 Hypergeometrictests and approximations 62 3.6.1 Lehmacher’sasymptotic hypergeometrictest 63 3.6.2 Ktichenhoff s continuity correction for Lehmacher’s test 64 3.7 Issuesof power and the selection of CFA tests 65 3.7.1 Naud’s power investigations 66 3.7.2 Applications of CFA tests 69 3.7.2.1 CFA of a sparsetable 70 3.7.2.2 CFA in a table with large frequencies 76 3.8 Selecting significance tests for CFA 78 3.9 Finding types and antitypes: Issuesof differential power 81 3.10 Methods of protecting a 85 3.10.1 The Bonferroni a protection (SS) 87 3.10.2 Holm’s procedurefor a protection (SD) 88 3.10.3 Hochberg’sprocedurefor a protection (SU) 89 List of contents 3.10.4 Holland and Copenhaver’sprocedurefor a protection &I 90 (SD) 3.10.5 Hommel, Lehmacher,and Perli’s modifications of 90 Holm’s procedurefor protection of the multiple level a (SD) 3.10.6 Illustrating the proceduresfor protecting the test-wise 92 a Descriptive Measures for Global CFA 97 4.1 The relative risk ratio, RR 97 4.2 The measure log P 98 4.3 Comparing the p component with the relative risk ratio and log P 99 Part II: Models and Applications of CFA 105 Global Models of CFA 105 5.1 Zero order global CFA 106 5.2 First order global CFA 110 5.2.1 Data exampleI: First order CFA of social network data 111 5.2.2 Data exampleII: First order CFA of Finkelstein’s Tanner data, Waves2 and 115 5.3 Secondorder global CFA 118 5.4 Third order global CFA 121 Regional Models of CFA 125 6.1 Interaction StructureAnalysis (ISA) 125 6.1.1 ISA of two groups of variables 126 6.1.2 ISA of three or more groups of variables 135 List of Contents -iv 6.2 Prediction CFA 139 6.2.1 Basemodels for Prediction CFA 139 6.2.2 More P-CFA models and approaches 152 6.2.2.1 Conditional P-CFA: Stratifying on a variable 152 6.2.2.2 Biprediction CFA 159 6.2.2.3 Prediction coefficients 164 Comparing k Samples 173 7.1 Two-sample CFA I: The original approach 173 7.2 Two-sample CFA II: Alternative methods 178 7.2.1 Gonzales-Deb&r’sX* 179 7.2.2 Goodman’sthree elementaryviews of nonindependence 180 7.2.3 Measuring effect strength in two-sampleCFA 186 7.3 Comparing three or more samples 190 7.4 Three groups of variables: ISA plus k-sampleCFA 195 Part III: Methods of Longitudinal CFA 203 CFA of Differences 205 8.1 A review of methodsof differences 206 8.2 The method of differences in CFA 212 8.2.1 Depicting the shapeof curves by differences: An example 213 8.2.2 Transformationsand the size of the table under study 214 8.2.3 Estimating expectedcell frequenciesfor CFA of differences 216 List of contents 41 8.2.3.1 Calculating a priori probabilities: Three examples 216 8.2.3.2 Three data examples 220 8.2.4 CFA of seconddifferences 227 CFA of Level, Variability, and Shape of Series of Observations 229 9.1 CFA of shifts in location 229 9.2 CFA of variability in a seriesof measures 236 9.3 Considering both level and trend in the analysisof seriesof measures 240 9.3.1 Estimation and CFA of polynomial parametersfor equidistant points on X 241 9.3.1.1 Orthogonal polynomials 244 9.3.1.2 Configural analysisof polynomial coefficients 248 9.3.2 Estimation and CFA of polynomial parametersfor non-equidistantpoints on X 251 9.4 CFA of seriesthat differ in length; an exampleof confirmatory CFA 256 9.5 Examining treatmenteffects using CFA; more confirmatory CFA 259 9.5.1 Treatmenteffects in pre-postdesigns(no control group) 259 9.5.2 Treatmenteffects in control group designs 263 9.6 CFA of patternsof correlation or multivariate distance sequences 265 9.6.1 CFA of autocorrelations 266 9.6.2 CFA of autodistances 269 List of Contents yj 9.7 Unidimensional CFA 271 9.8 Within-individual CFA 274 279 Part IV: The CFA Specialty File and Alternative Approaches to CFA 10 More Facets of CFA 280 10.1 CFA of cross-classificationswith structural zeros 280 10.2 The parsimony of CFA basemodels 284 10.3 CFA of groupsof cells: Searchingfor patternsof types and antitypes 293 10.4 CFA and the exploration of causality 295 10.4.1 Exploring the concept of the wedgeusing CFA ’ 296 10.4.2 Exploring the concept of thefork using CFA 301 10.4.3 Exploring the conceptof reciprocal causation using 305 CFA 10.5 Covariatesin CFA 309 10.5.1 Categorical covariates:stratification variables 309 10.52 Continuous covariates 316 10.6 CFA of ordinal variables 323 10.7 Graphical displays of CFA results 326 10.7.1 Displaying the patternsof types and antitypes basedon 327 test statistics or frequencies 10.7.2 Mosaic displays 330 10.8 Aggregating results from CFA 334 10.9 Employing CFA in tandemwith other methodsof analvsis 338 List of contents vii - 10.9.1 CFA and cluster analysis 338 10.9.2 CFA and discriminant analysis 342 11 Alternative Approaches to CFA 347 11.1 Kieser and Victor’s quasi-independencemodel of CFA 347 11.2 BayesianCFA 353 11.2.1 The prior and posterior distributions 354 11.2.2 Types and antitypes in BayesianCFA 356 11.2.3 Patternsof types and antitypes and protecting u 356 11.2.4 Data examples 357 Part V: Computational Issues 361 12 Software to Perform CFA 361 12.1 Using SYSTAT to perform CFA 362 12.1.1 SYSTAT’s two-way cross-tabulationmodule 362 12.1.2 SYSTAT’s log-linear modeling module 367 12.2 Using S-plusto perform BayesianCFA 371 12.3 Using CFA 2002 to perform FrequentistCFA 374 12.3.1 Program description 375 12.3.2 Sampleapplications 379 12.3.2.1First order CFA; keyboard input of frequencytable 379 12.3.2.2Two-sample CFA with two predictors; keyboard input 384 12.3.2.3SecondOrder CFA; data input via file 390 12.3.2.4CFA with covariates;input via file (Frequencies)and keyboard (covariate) 394 yllJ Part VI: List of Contents References, Appendices, and Indices 401 References 401 Appendix A: A brief introduction to log-linear modeling 423 Appendix B: Table of a*-levels for the Bonferroni and Holm 433 adjustments Author Index 439 Subject Index 445 Configural Frequency Analysis - Methods, Models, and Applications Preface Events that occur as expected are rarely deemedworth mentioning In contrast, events that are surprising, unexpected, unusual, shocking, or colossal appear in the news Examples of such events include terrorist attacks,when we are informed aboutthe eventsin New York, Washington, andPennsylvaniaon September11,2001; or on the more peacefulside,the weather, when we hear that there is a drought in the otherwise rainy Michigan; accidentstatistics,when we note that the numberof deathsfrom traffic accidents that involved alcohol is smaller in the year 2001 than expectedfrom earlier years;or health,whenwe learnthat smokingand lack of exercisein the population doesnot preventthe life expectancyin France from being one of the highest amongall industrial countries Configural FrequencyAnalysis (CFA) is a statistical method that allows one to determinewhether eventsthat are unexpectedin the sense exemplified aboveare significantly discrepantfrom expectancy.The idea is that for eachevent,an expectedfrequencyis determined.Then, one asks whether the observedfrequency differs from the expectedmore than just randomly As was indicated in the examples, discrepanciescome in two forms First, events occur more often than expected.For example, there may be more sunny days in Michigan than expected from the weather patternsusually observedin the Great Lakes region If such eventsoccur significantly more ofrenthan expected,the pattern under study constitutes a CFA type Other eventsoccur lessoften than expected.For example,one can ask whether the number of alcohol-relateddeathsin traffic accidents is significantIy below expectation.If this is the case,the patternunderstudy constitutesa CFA antitype According to Lehmacher (2000), questions similar to the ones answeredusing CFA, were asked already in 1922 by Pfaundler and von Sehr The authors asked whether symptoms of medical diseasescan be shown to co-occur aboveexpectancy.Lange and Vogel (1965) suggested that the term syndrom be used only if individual symptomsco-occurred above expectancy.Lienert, who is credited with the developmentof the conceptsand principles of CFA, proposedin 1968 (seeLienert, 1969) to test for eachcell in a cross-classificationwhether it constitutesa type or an antitype ix ... B: Table of a*-levels for the Bonferroni and Holm 433 adjustments Author Index 439 Subject Index 445 Configural Frequency Analysis - Methods, Models, and Applications Preface Events that occur... 2002 This page intentionally left blank Configural Frequency Analysis Methods, Models, and Applications This page intentionally left blank Part 1: Concepts and Methods of CFA This page intentionally... Base Models for CFA 19 2.1 SampleCFA basemodels and their designmatrices 22 2.2 Admissibility of log-linear models as CFA base models 27 2.3 Sampling schemesand admissibility of CFA base models