Log-Linear Models and Logistic Regression

The primary focus here is on log-linear models for contingency tables, but in this second edition, greater emphasis has been placed on logistic regression. The book explores topics such as logistic discrimination and generalised linear models, and builds upon the relationships between these basic models for continuous data and the analogous log-linear and logistic regression models for discrete data. It also carefully examines the differences in model interpretations and evaluations that occur due to the discrete nature of the data. Sample commands are given for analyses in SAS, BMFP, and GLIM, while numerous data sets from fields as diverse as engineering, education, sociology, and medicine are used to illustrate procedures and provide exercises. Throughoutthe book, the treatment is designed for students with prior knowledge of analysis of variance and regression.

[1]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[2]  J. Geweke,et al.  Bayesian Inference in Econometric Models Using Monte Carlo Integration , 1989 .

[3]  Otis Dudley Duncan,et al.  MULTIWAY CONTINGENCY ANALYSIS WITH A SCALED RESPONSE OR FACTOR , 1979 .

[4]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[5]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[6]  V. T. Farewell,et al.  Some results on the estimation of logistic models based on retrospective data , 1979 .

[7]  Nitin R. Patel,et al.  Computing Distributions for Exact Logistic Regression , 1987 .

[8]  W. Deming,et al.  On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known , 1940 .

[9]  H. O. Lancaster,et al.  The derivation and partition of chi2 in certain discrete distributions. , 1949, Biometrika.

[10]  Karl Pearson,et al.  ON THE SIGNIFICANCE OF THE TEACHER'S APPRECIATION OF GENERAL INTELLIGENCE , 1911 .

[11]  Leo A. Goodman,et al.  The analysis of multidimensional contingency tables when some variables are posterior to others: a modified path analysis approach , 1973 .

[12]  Elisa T. Lee,et al.  Statistical Methods for Survival Data Analysis , 1994, IEEE Transactions on Reliability.

[13]  D. Rubin.  Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician , 1984 .

[14]  J. O. Irwin.  A Note on the Subdividsion of ? 2 into Components , 1949 .

[15]  Seymour Geisser,et al.  Estimative influence measures for the multivariate general linear model , 1985 .

[16]  G. J. G. Upton,et al.  The statistical analysis of categorical data , 1992 .

[17]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[18]  James E. Grizzle,et al.  Log Linear Models and Tests of Independence for Contingency Tables , 1972 .

[19]  S. J. Press,et al.  Choosing between Logistic Regression and Discriminant Analysis , 1978 .

[20]  W. Johnson.  Influence measures for logistic regression: Another point of view , 1985 .

[21]  N. E. Breslow.  Statistical Methods in Cancer Research , 1986 .

[22]  Q. Mcnemar.  Note on the sampling error of the difference between correlated proportions or percentages , 1947, Psychometrika.

[23]  George E. P. Box,et al.  Sampling and Bayes' inference in scientific modelling and robustness , 1980 .

[24]  Edward B. Fowlkes,et al.  Risk analysis of the space shuttle: Pre-Challenger prediction of failure , 1989 .

[25]  D. Edwards,et al.  A fast procedure for model search in multidimensional contingency tables , 1985 .

[26]  E. Bedrick.  Adjusted chi-squared tests for cross-classified tables of survey data , 1983 .

[27]  L. A. Goodman.  The Multivariate Analysis of Qualitative Data: Interactions among Multiple Classifications , 1970 .

[28]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[29]  D. Edwards.  Introduction to graphical modelling , 1995 .

[30]  D. Pregibon.  Logistic Regression Diagnostics , 1981 .

[31]  Otis Dudley Duncan,et al.  Partitioning polytomous variables in multiway contigency analysis , 1975 .

[32]  K. Chaloner,et al.  A Bayesian approach to outlier detection and residual analysis , 1988 .

[33]  Hsin Ying Lin,et al.  Bayesian estimation of item response curves , 1986 .

[34]  Morton B. Brown.  Screening Effects in Multidimensional Contingency Tables , 1976 .

[35]  D. M. Titterington,et al.  Neural Networks: A Review from a Statistical Perspective , 1994 .

[36]  J. E. H. Shaw,et al.  The implementation of the bayesian paradigm , 1985 .

[37]  Anthony C. Davison,et al.  Approximate conditional inference in generalized linear models , 1988 .

[38]  L. A. Goodman.  Partitioning of Chi-Square, Analysis of Marginal Contingency Tables, and Estimation of Expected Frequencies in Multidimensional Contingency Tables , 1971 .

[39]  Howard Schuman,et al.  Social change in a metropolitan community , 1973 .

[40]  Tom Leonard.  Bayesian methods for binomial data , 1972 .

[41]  J. Tukey,et al.  Transformations Related to the Angular and the Square Root , 1950 .

[42]  M. Lawera.  Predictive inference : an introduction , 1995 .

[43]  K. Larntz.  Small-Sample Comparisons of Exact Levels for Chi-Squared Goodness-of-Fit Statistics , 1978 .

[44]  Peter A. Lachenbruch,et al.  Robustness of the linear and quadratic discriminant function to certain types of non‐normality , 1973 .

[45]  R. Dennis Cook,et al.  Assessing influence on regression coefficients in generalized linear models , 1989 .

[46]  Blaschke.  Das Gesetz der kleinen Zahlen , 1898 .

[47]  T. Speed,et al.  Recursive causal models , 1984, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[48]  David W. Hosmer,et al.  Applied Logistic Regression , 1991 .

[49]  Susan Quine.  Achievement orientation of aboriginal and white Australian adolescents , 1973 .

[50]  Erling B. Andersen.  Diagnostics in categorical data analysis , 1992 .

[51]  Jeffrey S. Simonoff,et al.  An Improved Goodness-of-Fit Statistic for Sparse Multinomials , 1985 .

[52]  T. Havránek.  A Procedure for Model Search in Multidimensional Contingency Tables , 1984 .

[53]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis, 2nd Edition. , 1985 .

[54]  Nitin R. Patel,et al.  A Network Algorithm for Performing Fisher's Exact Test in r × c Contingency Tables , 1983 .

[55]  H. F. Martz,et al.  The risk of catastrophic failure of the solid rocket boosters on the space shuttle , 1992 .

[56]  John Bibby,et al.  The Analysis of Contingency Tables , 1978 .

[57]  J. K. Benedetti,et al.  Strategies for the selection of log-linear models. , 1978, Biometrics.

[58]  Gary G. Koch,et al.  An Incomplete Contingency Table Approach to Paired-Comparison Experiments , 1976 .

[59]  J. Naylor,et al.  Applications of a Method for the Efficient Computation of Posterior Distributions , 1982 .

[60]  T. Speed,et al.  Structural Analysis of Multivariate Data: A Review , 1982 .

[61]  Timothy R. C. Read,et al.  Goodness-Of-Fit Statistics for Discrete Multivariate Data , 1988 .

[62]  Gary G. Koch,et al.  Strategies in the Multivariate Analysis of Data from Complex Surveys , 1975 .

[63]  H. Dennis Tolley,et al.  The asymptotic covariance structure of estimated parameters from contingency table log-linear models , 1975 .

[64]  P. Holland,et al.  Discrete Multivariate Analysis. , 1976 .

[65]  Marcello Pagano,et al.  An Algorithm for Finding the Exact Significance Levels of r × c Contingency Tables , 1981 .

[66]  H. Waite.  THE TEACHER'S ESTIMATION OF THE GENERAL INTELLIGENCE OF SCHOOL CHILDREN , 1911 .

[67]  John Aitchison,et al.  Statistical Prediction Analysis , 1975 .

[68]  R. Pyke,et al.  Logistic disease incidence models and case-control studies , 1979 .

[69]  Dennis E. Jennings.  Outliers and Residual Distributions in Logistic Regression , 1986 .

[70]  Peter E. Rossi,et al.  Bayesian analysis of dichotomous quantal response models , 1984 .

[71]  W. F. Gross.  A Note on “Chi‐Squared Tests with Survey Data” , 1984 .

[72]  L. A. Goodman.  Simple Models for the Analysis of Association in Cross-Classifications Having Ordered Categories , 1979 .

[73]  Murray Aitkin,et al.  The Analysis of Unbalanced Cross-classifications , 1978 .

[74]  D. J. Finney,et al.  The estimation from individual records of the relationship between dose and quantal response. , 1947, Biometrika.

[75]  J. Wing,et al.  Institutionalism in mental hospitals. , 1962, The British journal of social and clinical psychology.

[76]  Charles J. Geyer,et al.  Practical Markov Chain Monte Carlo , 1992 .

[77]  A. Hossain,et al.  A comparative study on detection of influential observations in linear regression , 1991 .

[78]  C R Mehta,et al.  The exact analysis of contingency tables in medical research , 1994, Statistical methods in medical research.

[79]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS THE METHOD OF PAIRED COMPARISONS , 1952 .

[80]  Franklin A. Graybill,et al.  An Analysis of a Two-Way Model with Interaction and No Replication , 1972 .

[81]  A. F. Brunswick,et al.  Adolescent health, sex, and fertility. , 1971, American journal of public health.

[82]  R. Christensen.  Linear Models for Multivariate, Time Series, and Spatial Data , 1997 .

[83]  J. Anderson.  Separate sample logistic discrimination , 1972 .

[84]  D. Edwards,et al.  The analysis of contingency tables by graphical models , 1983 .

[85]  G. McLachlan.  Discriminant Analysis and Statistical Pattern Recognition , 1992 .

[86]  P. Moran.  On the method of paired comparisons. , 1947, Biometrika.

[87]  D. Edwards,et al.  Collapsibility and response variables in contingency tables , 1983 .

[88]  Svend Kreiner,et al.  Analysis of Multidimensional Contingency Tables by Exact Conditional Tests: Techniques and Strategies , 1987 .

[89]  Arjun K. Gupta.  The Theory of Linear Models and Multivariate Analysis , 1981 .

[90]  Shelby J. Haberman,et al.  The Analysis of Nonadditivity in Two-Way Analysis of Variance , 1990 .

[91]  G. Yule.  On the Association of Attributes in Statistics: With Illustrations from the Material of the Childhood Society, &c , 1900 .

[92]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[93]  Cyrus R. Mehta,et al.  Computing an Exact Confidence Interval for the Common Odds Ratio in Several 2×2 Contingency Tables , 1985 .

[94]  Ronald Christensen,et al.  Analysis of Variance, Design, and Regression: Applied Statistical Methods , 1996 .

[95]  T. Speed,et al.  Markov Fields and Log-Linear Interaction Models for Contingency Tables , 1980 .

[96]  Lennart Nordberg,et al.  On variable selection in generalized linear and related regression models , 1982 .

[97]  Murray Aitkin,et al.  A Simultaneous Test Procedure for Contingency Table Models , 1979 .

[98]  M. Plummer,et al.  International agency for research on cancer. , 2020, Archives of pathology.

[99]  M. Bartlett.  Contingency Table Interactions , 1935 .

[100]  S. Haberman.  Analysis of qualitative data , 1978 .

[101]  Stephen E. Fienberg,et al.  The analysis of cross-classified categorical data , 1980 .

[102]  James M. Boyett,et al.  Random RxC tables with given row and column totals , 1979 .

[103]  H. Foreman,et al.  Premarital contraceptive usage: a study and some theoretical explorations. , 1975 .

[104]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[105]  W. Haenszel,et al.  Statistical aspects of the analysis of data from retrospective studies of disease. , 1959, Journal of the National Cancer Institute.

[106]  D. Pregibon,et al.  Graphical Methods for Assessing Logistic Regression Models , 1984 .

[107]  A. Agresti.  [A Survey of Exact Inference for Contingency Tables]: Rejoinder , 1992 .

[108]  S. Haberman,et al.  The analysis of frequency data , 1974 .

[109]  J. Mandel.  A New Analysis of Variance Model for Non-additive Data , 1971 .

[110]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[111]  P. Holland.  Statistics and Causal Inference , 1985 .

[112]  Cyrus R. Mehta,et al.  A network algorithm for the exact treatment of the 2×k contingency table , 1980 .

[113]  A A Tsiatis,et al.  Exact significance testing to establish treatment equivalence with ordered categorical data. , 1984, Biometrics.

[114]  A. Scott,et al.  On Chi-Squared Tests for Multiway Contingency Tables with Cell Proportions Estimated from Survey Data , 1984 .

[115]  M Zelen,et al.  Estimation of exponential survival probabilities with concomitant information. , 1965, Biometrics.

[116]  Guido del Pino,et al.  The Unifying Role of Iterative Generalized Least Squares in Statistical Algorithms , 1989 .

[117]  Chris J. Skinner,et al.  Analysis of complex surveys , 1991 .

[118]  J. Rao,et al.  Small-Sample Comparisons of Level and Power for Simple Goodness-of-Fit Statistics under Cluster Sampling , 1987 .

[119]  Ronald Christensen,et al.  Plane Answers to Complex Questions: The Theory of Linear Models , 1989 .

[120]  J. Anderson,et al.  Penalized maximum likelihood estimation in logistic regression and discrimination , 1982 .

[121]  Frederick Mosteller,et al.  Data Analysis and Regression , 1978 .

[122]  Shelby J. Haberman,et al.  Log-Linear Models for Frequency Tables with Ordered Classifications , 1974 .

[123]  David J. Hand,et al.  Discrimination and Classification , 1982 .

[124]  M. Kendall.  Statistical Methods for Research Workers , 1937, Nature.

[125]  Peter McCullagh,et al.  The Conditional Distribution of Goodness-of-Fit Statistics for Discrete Data , 1986 .

[126]  M. M. Meyer.  Transforming Contingency Tables , 1982 .

[127]  Leo A. Goodman,et al.  Association Models and Canonical Correlation in the Analysis of Cross-Classifications Having Ordered Categories , 1981 .

[128]  G. Koch,et al.  Analysis of categorical data by linear models. , 1969, Biometrics.

[129]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[130]  A. Tsiatis.  A note on a goodness-of-fit test for the logistic regression model , 1980 .

[131]  S. Geisser,et al.  A Predictive View of the Detection and Characterization of Influential Observations in Regression Analysis , 1983 .

[132]  A. Bonato,et al.  Graphs and Hypergraphs , 2021, Clustering.

[133]  Alan Agresti,et al.  Exact conditional tests for cross-classifications: Approximation of attained significance levels , 1979 .

[134]  Seymour Geisser,et al.  8. Predictive Inference: An Introduction , 1995 .

[135]  Robert Bartle,et al.  The Elements of Real Analysis , 1977, The Mathematical Gazette.

[136]  N. Wermuth,et al.  Graphical and recursive models for contingency tables , 1983 .

[137]  A. Scott,et al.  Chi-squared Tests with Survey Data , 1980 .

[138]  Franklin A. Graybill,et al.  Extensions of the General Linear Hypothesis Model , 1970 .

[139]  Fred W. Roush.  Discrete statistical models with social science applications: Erling B. Andersen, Amsterdam: North-Holland , 1981 .

[140]  A. Scott,et al.  The Analysis of Categorical Data from Complex Sample Surveys: Chi-Squared Tests for Goodness of Fit and Independence in Two-Way Tables , 1981 .

[141]  P. McCullagh.  Analysis of Ordinal Categorical Data , 1985 .

[142]  Adrian F. M. Smith,et al.  Bayesian Inference for Generalized Linear and Proportional Hazards Models Via Gibbs Sampling , 1993 .

[143]  Michael L. Radelet,et al.  Racial Characteristics and the Imposition of the Death Penalty. , 1981 .

[144]  Bradley P. Carlin,et al.  BAYES AND EMPIRICAL BAYES METHODS FOR DATA ANALYSIS , 1996, Stat. Comput..

[145]  S. Fienberg,et al.  Log linear representation for paired and multiple comparisons models , 1976 .

[146]  S. Geisser.  Aspects of the Predictive and Estimative Approaches in the Determination of Probabilities , 1982 .

[147]  P. Bickel,et al.  Sex Bias in Graduate Admissions: Data from Berkeley , 1975, Science.

[148]  C. Chuang,et al.  Multiplicative-interaction logit models for i×j×2 three-way tables , 1983 .

[149]  Shelby J. Haberman,et al.  Log-Linear Models and Frequency Tables with Small Expected Cell Counts , 1977 .

[150]  Bernard Lazerwitz,et al.  A Comparison of Major United States Religious Groups , 1961 .

[151]  J. N. R. Jeffers,et al.  Graphical Models in Applied Multivariate Statistics. , 1990 .

[152]  R. Christensen,et al.  A New Perspective on Priors for Generalized Linear Models , 1996 .

[153]  Ronald Christensen,et al.  Testing for nonadditivity in log-linear and logit models , 1992 .

[154]  Richard Scheines,et al.  Discovering Causal Structure: Artificial Intelligence, Philosophy of Science, and Statistical Modeling , 1987 .

[155]  B. Efron.  The Efficiency of Logistic Regression Compared to Normal Discriminant Analysis , 1975 .

[156]  Erling B. Andersen,et al.  Discrete Statistical Models with Social Science Applications. , 1980 .

[157]  Edward J. Bedrick,et al.  Outlier tests for logistic regression: A conditional approach , 1990 .

[158]  L. Tierney,et al.  Accurate Approximations for Posterior Moments and Marginal Densities , 1986 .

[159]  Stephen E. Fienberg,et al.  The Use of Chi‐Squared Statistics for Categorical Data Problems , 1979 .

[160]  K. Koehler.  Goodness-of-fit tests for log-linear models in sparse contingency tables , 1986 .

[161]  Timothy R. C. Read,et al.  Multinomial goodness-of-fit tests , 1984 .

[162]  Robert E. Fay,et al.  A Jackknifed Chi-Squared Test for Complex Samples , 1985 .

[163]  Gail Gong.  Cross-Validation, the Jackknife, and the Bootstrap: Excess Error Estimation in Forward Logistic Regression , 1986 .

[164]  Kosuke Imai,et al.  Survey Sampling , 1998, Nov/Dec 2017.

[165]  Alan E. Gelfand,et al.  Bayesian statistics without tears: A sampling-resampling perspective , 1992 .

[166]  M. W. Birch.  Maximum Likelihood in Three-Way Contingency Tables , 1963 .

[167]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS , 1952 .

[168]  Joseph Berkson,et al.  In dispraise of the exact test: Do the marginal totals of the 2X2 table contain relevant information respecting the table proportions? , 1978 .

[169]  D. G. Simpson,et al.  The Statistical Analysis of Discrete Data , 1989 .

[170]  D. W. Balmer,et al.  Algorithm AS 236: recursive enumeration of r×c tables for exact likelihood evaluation , 1988 .

[171]  S. Brier.  Analysis of contingency tables under cluster sampling , 1980 .

[172]  N. Wermuth.  Model Search among Multiplicative Models , 1976 .

[173]  Oscar Kempthorne,et al.  In dispraise of the exact test: reactions☆ , 1979 .