Salient features are outlined of hierarchical log-linear models appropriate to the analysis of associations between categorical variables. Comparisons are made with alternative methods, and the rationale of the Aitkin simultaneous test procedure for minimal model selection is discussed in detail and compared with screening and stepwise selection strategies.
Get full access to this article
View all access options for this article.
References
1.
AitkinM, 1978“The analysis of unbalanced cross-classifications”Journal of the Royal Statistical Society, Series A141195–223
2.
AitkinM, 1979“A simultaneous test procedure for contingency table models”Journal of the Royal Statistical Society, Series C28233–242
3.
AitkinM, 1980“A note on the selection of log-linear models”Biometrics36173–178
4.
AlthamP M E, 1979“Detecting relationships between categorical variables over time: A problem of deflating a chi-squared statistic”Applied Statistics28115–125
5.
BerksonJ, 1953“A statistically precise and relatively simple method of estimating the bio-assay with quantal response based on the logistic function”Journal of the American Statistical Association48565–599
6.
BerksonJ, 1955“Maximum likelihood and minimum X2 estimates of the logistic function”Journal of the American Statistical Association50130–162
7.
BerksonJ, 1980“Minimum chi-square, not maximum likelihood (with discussion)”Annals of Statistics8(3) 457–487
8.
BishopY M MFienbergS EHollandP W, 1975Discrete Multivariate Analysis: Theory and Practice (MIT Press, Cambridge, Mass)
9.
BlythC R, 1972“On Simpson's paradox and the sure-thing principle”Journal of the American Statistical Association67364–366
10.
BrownM B, 1976“Screening effects in multidimensional contingency tables”Applied Statistics2537–46
11.
FienbergS E, 1980The Analysis of Cross-classified Categorical Data (MIT Press, Cambridge, Mass)
12.
FingletonB, 1975“A factorial approach to the nearest centre hypothesis”Transactions of the Institute of British Geographers65131–139
13.
FingletonB, 1980“Some log-linear models of spatial behaviour” paper presented to the Institute of British Geographers Quantitative Methods Study Group, Lancaster University, 1980; available from the author
14.
FingletonB, 1981“Log-linear models, mostellerizing and forecasting”Area13(2) 123–129
15.
GoodmanL A, 1973“The analysis of multidimensional contingency tables when some variables are posterior to others: A modified path analysis approach”Biometrika60179–192
16.
GoodmanL A, 1978Analyzing Qualitative/Categorical Data (Cambridge, Mass)
17.
GrizzleJ EStarmerC FKochG G, 1969“Analysis of categorical data by linear models”Biometrics25489–504
18.
HoltD, 1979“Log-linear models for contingency table analysis: On the interpretation of parameters”Sociological Methods and Research7330–336
19.
IrelandC TKuH HKullbackS, 1969“Symmetry and marginal homogeneity of an r × r contingency table”Journal of the American Statistical Association641323–1341
20.
NeymanJ, 1949“Contributions to the theory of the x2 test” in Proceedings of the First Berkeley Symposium on Mathematical Statistics and Probability Ed. NeymanJ (University of California Press, Berkeley, Calif.) pp 230–273
21.
O'BrienL GWrigleyN, 1980“Computer programs for the analysis of categorical data”Area12(4) 263–268
22.
PlackettR L, 1974The Analysis of Categorical Data (Charles Griffin, High Wycombe, Bucks)
23.
SimpsonE H, 1951“The interpretation of interaction in contingency tables”Journal of the Royal Statistical Society, Series B13238–241
24.
StapletonC M, 1980“Limitations of log-linear models in geography”Transactions of the Institute of British Geographers5502–508
25.
TheilH, 1970“On the estimation of relationships involving qualitative variables”American Journal of Sociology76103–154
26.
UptonG J G, 1978The Analysis of Cross-tabulated Data (John Wiley, Chichester, Sussex)