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Fienberg S.E. Analysis of Cross-Classified Categorical Data
Fienberg S.E.  Analysis of Cross-Classified Categorical Data









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: Analysis of Cross-Classified Categorical Data

: Fienberg S.E.

:

A variety of biological and social science data come in the form of cross-classified tables of counts, commonly referred to as contingency tables. Until recent years the statistical and computational techniques available for the analysis of cross-classified data were quite limited. This book presents some of the recent work on the statistical analysis of cross-classified data using longlinear models, especially in the multidimensional situation.


: en

: /

:

ed2k: ed2k stats

: Second Edition

: 2007

: 216

: 01.07.2008

: | | ID
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$G^2$      see Likelihood-ratio statistic
Additive models      5
Aitkin, M.A.      80 177
Altham, P.M.E.      32 177
Analysis of covariance      3 see
Andersen, A.H.      167 177
Anderson, J.A.      137 177
Anderson, J.B.      17 177
ANOVA, analogies with      34
Antecedent variables      123 see
Arc sine transformation      23
Armitage, P.      23 177
Ashford, J.R.      66 67 177
Association, measures of      see Cross-product ratio
Asymptotic standard errors      8384 88 104 170
Banwart, A.      121 188
Bartlett, M.S.      1 5 36 177
Baseball wins and losses      152154
Beaton, A.E.      45 177
Benedetti, J.K.      80 177
Berkson, J.      6 22 177
Bhapkar, V.P.      6 31 88 177
Bickel, P.J.      53 177
Binary response      6 see univariate
Binomial distribution, comparing two proportions      810 1315
Binomial distribution, for paired comparisons      150152
Birch, M.W.      6 31 33 177
Bishop, Y.M.M.      xi 2 5 6 19 23 33 38 39 49 56 60 71 73 74 83 84 96 97 98 99 117 142 143 144 147 150 153 166 175 177 178
Blalock, H.M., Jr.      1 121 178
Bliss, C.I.      1 95 178
Bloomfield, P.      43 178
Blyth, C.R.      50 178
Bock, R.D.      2 6 62 88 178
Bradley Terry model      150154
Brier, S.S.      32 134 178
Brown, D.T.      38 81 178
Brown, M.B.      56 80 177 178
Brunswick, A.F.      148 178
Bunker, J.P.      5 6 179
Campbell, B.J.      90 184
Causal analysis      120138
Chen, T.T.      113 142 179
Chi-square distribution, percentage points of      171
Clayton, D.G.      62 179
Closed-form estimates      see Direct estimates
cluster sampling      32
Cochran, W.G.      1 48 136 179 188
Cohen, J.E.      32 179
Coleman, J.S.      125 126 179
collapsing tables      4851 153156
Complex-sample survey data      3132
conditional tests      5758 81
Conover, W.J.      22 179
Consistent estimator      106 166
Continuation ratios      110111 114116
Continuous explanatory variables      see Logit model continuous
Contrasts      see Linear contrast
Cornfield, J.      6 17 105 179 189
Correction for continuity      2122
Cox, D.R.      xi 2 3 6 22 23 71 85 98 101 102 165 179
Cross-product ratio as linear contrast      16 19
Cross-product ratio, association measures based on      18
Cross-product ratio, asymptotic variance of      18
Cross-product ratio, definition of      17
Cross-product ratio, equality of      3637
Cross-product ratio, historical development      45
Cross-product ratio, interpretation of      17
Cross-product ratio, invariance      17 135
Cross-product ratio, properties of      17 135
Cross-product ratio, related to u-terms      16 19
Cross-product ratio, use in substantive fields      17
Daniel, C.      85 179
Darroch, J.N.      5 6 38 49 51 60 63 180
Davidovits, P.      17 177
Dawber, T.R.      6 180
Degrees of freedom, adjusting for empty cells      142
Degrees of freedom, for complete tables      7475
Degrees of freedom, for quasi-independence      145
Degrees of freedom, for three-dimensional models      41
Degrees of freedom, general formula      40 142
Delta method      83
Deming, W.E.      38 180
Deming-Stephan procedure      see Fitting iterative
Dempster, A.P.      2 3 180
Descriptive level of significance      165166
Design effect      32
Deviance      see Likelihood-ratio statistic
Dillon, W.R.      106 182
Direct estimates, asymptotic variances for      170
Direct estimates, asymptotic variances for complete tables      3234 7273
Direct estimates, differences between models      6061
Direct estimates, equivalence to iteration      3940
Direct estimates, partitioning $G^2$ for models with      6061
Discriminant analysis      105109
Doering, C.R.      84 186
Draper, N.R.      80 180
DuMouchel, W.      99 180
Duncan, B.      54 180
Duncan, D.B.      3 104 111 189
Duncan, O.D.      54 120 134 153 155 156 180
Dyke Patterson data      8488 9899
Dyke, G.V.      84 85 86 180
Dykes, M.H.M.      9 180
Efron, B.      104 118 180
Empty cells      see Zero entries
Epidemiological studies      67 31 135137
Estimated expected values      see Maximum-likelihood estimates
Estimation, methods of      56
Exact tests      see Hypergeometric distribution
Explanatory variables      2 15
Farewell, V.T.      137 180
Fay, R.E., III      32 181
Fellegi, I.      32 181
Feller, W.      15 181
Fetal monitoring data      104105 117
Fienberg, S.E.      xi 2 5 6 19 23 25 33 38 39 49 52 56 60 71 73 83 104 105 106 111 113 117 142 143 144 147 150 151 152 153 166 172 175 178 179 181 187
Fisher, F.M.      134 181
Fisher, R.A.      15 181
Fitting, iterative proportional, comparison with Newton Raphson, algorithm      63 64 103104
Fitting, iterative proportional, complete tables      3740 74
Fitting, iterative proportional, convergence of      38
Fitting, iterative proportional, incomplete tables      144145 147148
Fitting, iterative proportional, ordered categories      6366
Fleiss, J.L.      1 181
Foreman, H      121 188
Forrest, W.H., Jr.      5 6 179
Fourfold table ($2 \times 2$ table), descriptive parameters of      815 1619
Framingham study      67
Frankel, M.R.      32 184
Freedman, D.      53 182
Freeman, D.H., Jr.      32 88 169 170 184 185
Freeman, J.L.      32 184
Friedman, E.A.      104 105 106 187
Gait, J.J.      18 182
Generalized iterative scaling      6366
Gokhale, D.V.      2 38 104 182
Goldberger, A.S.      134 182
Goldstein, M.      106 182
Good, I.J.      6 72 182
Goodman, L.A.      2 5 6 18 56 57 60 61 63 71 73 74 77 79 80 83 84 97 120 123 125 128 138 143 157 158 159 182 183
Goodness-of-fit, asymptotic distribution of test statistics for      40 see
Gottfredson, M.R.      93 189
Greenland, S.      104 105 106 187
Grizzle, J.E.      2 6 22 37 62 136 148 149 183
Guttman scaling      155159
Haberman, S.J.      xi 2 3 22 23 31 38 43 62 64 66 88 101 102 103 104 143 144 147 167 168 175 183 184
Hagen, E.P.      44 189
Half-normal plot      86
Hamdan, M.A.      4 185
Hammel, E.A.      53 177
Hansen, W.L.      112 184
Hartley, H.O.      171 187
Heckman, J.J.      134 184
Heron, D.      5 187
Hewlett, P.S.      23 184
Hierarchical models      43 7273
Hierarchy of models      5758 65 6869
Hierarchy principle      43
Hinkley, D.V.      165 179
Hoaglin, D.      171 184
Hocking, R.R.      113 184
Holland, P.W.      xi 2 5 6 19 23 33 38 39 49 60 71 73 83 117 142 143 144 147 153 166 175 178
Homogeneity of proportions      13
Hoyt, C.J.      91 184
Hypergeometric distribution      22 31
Imrey, P.B.      160 184
Incomplete arrays      142150
Independence, conditional      28
Independence, for $2 \times 2$ tables      1013
Independence, in rectangular arrays      1315
Independence, in three-dimensional arrays      2728
Independence, possible models of      72
Independence, quasi-independence      142146
Indirect estimates      see Fitting iterative
Intervening variable      123
Ireland, C.T.      38 184
Iterative proportional fitting      see Fitting iterative
Iterative scaling      see Fitting iterative
Jennrich, R.I.      101 184
Johnson, W.D.      160 184
Jureen, L.      124 189
Kannel, W.B.      6 105 180 189
Kastenbaum, M.      5 6 184 188
Katz, B.M.      69 184
Kempthorne, O.      22 184
Kihlberg, J.K.      90 184
Killion, R.A.      6 184
Kimura, M.L.      17 184
Kish, L.      32 184
Koch, G.G.      2 6 31 32 37 62 88 160 169 170 177 183 184 185
Koehler, K.J.      175 185
Krishnaiah, P.R.      91 184
Kruskal, W.H.      5 18 56 183 185
Ku, H.H.      2 56 60 88 185
Kullback, S.      2 38 56 60 88 136 182 184 185
Kupperman, M.      60 185
Lancaster, H.O.      2 4 60 185
Larntz, K.      41 144 151 162 172 173 174 181 185
Lauh, E.      71 85 179
Least squares, weighted      99 101 104
Lee, S.K.      88 170 174 185
Lerman, S.R.      136 186
Light, K.J.      172 186
Likelihood-ratio statistic, $G^2$      see also Partitioning chi-square likelihood
Likelihood-ratio statistic, asymptotic distribution of      40 166 174176
Likelihood-ratio statistic, compared with Pearson's chi-square statistic      4041 172173
Likelihood-ratio statistic, definition of      40
Likelihood-ratio statistic, differences of, for nested models      5657 175176
Likelihood-ratio statistic, small-sample behavior of      172174
Lindley, D.V.      51 83 185 186
Lindsey, J.K.      xi 2 186
Linear contrast      see also Loglinear model; u-terms
Linear contrast, asymptotic variance of      8284
Linear contrast, definition of      82
Lizard data      1113 2729 3540 4243
Logistic regression      see Logistic response function
Logistic response function      see Logit model
Logistic response function, comparison with discriminant, function      105109
Logistic response function, multivariate      110116
Logistic response function, univariate      22 102109
Logit model, assessment of predictive ability      99 104
Logit model, categorical predictors      9599
Logit model, continuous predictors      102109
Logit model, definition of      96
Logit model, nonrecursive systems of      133134
Logit model, ordered categorical predictors      99102
Logit model, recursive systems of      123133
Logit model, simultaneous equations model involving      133134
Loglinear contrast      see Linear contrast
Loglinear model      see also Linear contrast; Cross-product ratio; Direct estimates
Loglinear model, for $2 \times 2 \times 2$ table      2729
Loglinear model, for $I \times J$ table      1315
Loglinear model, general      29 7177
Lombard, H.L.      84 186
Lyell, L.P.      6 180
Mallar, C.D.      134 186
Manski, C.F.      136 186
Marginal totals, analyses on      2021
Marginal totals, fixed, by conditioning      9799
Marginal totals, fixed, by design      9596
Marginality constraints      see Hierarchical models
Margolin, B.H.      172 186
Mason, W.M.      111 112 181 189
Maximum-likelihood estimates for higher-dimensional tables      7177
Maximum-likelihood estimates for incomplete tables      142150
Maximum-likelihood estimates for independence      13
Maximum-likelihood estimates for loglinear models with ordered categories      6168
Maximum-likelihood estimates for three-dimensional loglinear models      3240
Maximum-likelihood estimation, definition of      165166
Maximum-likelihood estimation, equivalence of      1516 31
Maximum-likelihood estimation, existence of      168
Maximum-likelihood estimation, for multinomial      169
Maximum-likelihood estimation, for Poisson      167
Maximum-likelihood estimation, for product-multinomial      169
Maxwell, A.E.      1 186
McFadden, D.      136 186
McHugh, R.B.      161 186
Meehl, P.E.      51 186
Meier, P.      9 180
Minimal sufficient statistics      see Sufficient statistics minimal
Minimum modified chi-square statistic      37
Missing observations      113 160
Mitra, S.K.      5 188
MLE      see Maximum-likelihood estimates
Model      see Loglinear model
Model, selection of      5661 7780
Model, simplicity in building a      56
Moore, R.H.      101 184
Morgan, B.J.T.      160 186
Morris, C.      175 186
Mosteller, F.      5 6 17 99 152 178 179 186
Multinomial distribution, asymptotic Multinomial distribution, variance of loglinear contrasts for      8284
Multinomial distribution, estimation for      3031 168169
Multinomial distribution, product-multinomial      15 3031 168169
Multinomial distribution, sampling distribution      15 30 31
Multivariate analysis, forms of      24
Muthen, B.      134 186
Narragon, E.A.      90 184
National Halothane Study      6 99
NBER TH data      2021 4448 61 149151
Nelder, J.A.      43 99 101 104 186 187
Nerlove, M.      3 62 104 134 187
Nested models, differences in $G^2$      5657
Neutra, R.R.      104 105 106 187
Newton Raphson algorithm      6364 66 104
Newton's method, unidimensional      63
Novick, M.R.      51 186
O'Connell, J.W.      53 177
Odds ratio      105 see
Odoroff, C.L.      172 187
Ordered categories      6168 99102
Owens, M.W.B.      32 187
Oxspring, H.R      113 184
Paired comparisons      150154
Parameters      see u-terms
Parsimony      56
Partitioning chi-square, Lancaster's method      4 5 60
Partitioning chi-square, likelihood ratio      5761 7477
Path diagrams      120123 128
Patterson, H.D.      84 85 86 180
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