Hosmer D.W., Lemeshow S. — Applied logistic regression :: Электронная библиотека попечительского совета мехмата МГУ

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Hosmer D.W., Lemeshow S. — Applied logistic regression

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Название: Applied logistic regression

Авторы: Hosmer D.W., Lemeshow S.

Аннотация:

A textbook for part of a graduate survey course, courses of a quarter or semester, and focused short courses for working professionals. Assuming a solid foundation in linear regression methodology and contingency table analysis, biostaticians Hosmer (U. of Massachusetts- Amherst) and Lemeshow (Ohio State U.) introduce the logistic regression model and its use in methods for modeling the relationship between a categorical outcome variable and a set of covariates. The first edition appeared about a decade ago, and the second incorporates theoretical and computational developments since then.

Язык:

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 2000

Количество страниц: 376

Добавлена в каталог: 03.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$2\times2$ tables, generally: classification      159—160 228
$2\times2$ tables, generally: contingency      331
$2\times2$ tables, generally: fitted logistic regression compared with stratified analysis      79—85
$2\times2$ tables, generally: model-building strategies      136—137
      131 164—167 345
1—1 matched study: example of      230—235
1—1 matched study: goodness-of-fit assessment      236—243
1—1 matched study: logistic regression analysis for      226—230
1—M matched study: example of      243—248
1—M matched study: goodness-of-fit assessment      248—259
Additive models      103—104
Adjacent-category logistic model      289 293—295 297—298
Adjustment, statistical      65 67 69
Algorithms, variable selection      96
Analysis of covariance      65
Analysis of variance table      11—12
Asthma study, correlated data analysis      309—312
Asymptotic distribution      132
Asymptotically equivalent      21
Auto-regressive mode, correlated data analysis      313
Baseline logit model      289
Best subsets linear regression, model-building: applications, generatly      128—129
Best subsets linear regression, model-building: interaction      136—137
Best subsets linear regression, model-building: matrix notation      128—131
Best subsets linear regression, model-building: multivariable analysis      132
Best subsets linear regression, model-building: overfitting      134—135
Best subsets linear regression, model-building: sum-of-squares      130—131
Best subsets linear regression, model-building: UIS case illustration      132—135
Best subsets linear regression, model-building: univariate stage      129—130
Best subsets linear regression, model-building: variable selection      96
Best subsets linear regression, model-building: vector notation      128—129
Binary logistic models      1 278 307—308
Binomial distribution      7 116
BMDPLR      121—122
Breslow — Day test      83—84
Calibration, goodness-of-fit assessment      159
Case-control studies: components of      189—190 205—210
Case-control studies: matched      See Matched case-control studies
Chi-square distribution: best subsets logistic regression      133
Chi-square distribution: fitted logistic regression      72 82 85
Chi-square distribution: logistic regression      14 16
Chi-square test, variable selection: benefits of      92—93 102
Chi-square test, variable selection: stepwise logistic regression      116
Classification      21
Classification tables, goodness-of-fit assessment      156—160 188
Cluster-level covariates      309
Cluster-specific model, correlated data analysis      310—312 316—317 320—328
Clustering      185—186
Coefficients, generally: correlated      See Correlated data analysis
Coefficients, generally: in variable selection      97
Coefficients, generally: testing for significance of      11—17
Cohort studies      203—205
Collinearity      140—141
Complex sample surveys, fitting logistic regression models to data from      211—221
Conditional exact maximum likelihood estimate (CMLE)      334—337
Conditional maximum likelihood estimators      23
Conditional mean      4 6—7 168
Confidence interval estimation: fitted logistic regression      52—53 55 62 88
Confidence interval estimation: logistic regression      17—21
Confidence interval estimation: multiple logistic regression      35 40—42
Confidence interval: estimation      See Confidence interval estimation
Confidence interval: in goodness-of-fit assessment      191 195—198
Confidence interval: Wald-based      19—20
Confidence limits      59
Confounding: fitted logistic regression      70—74
Confounding: goodness-of-fit assessment      185
Confounding: variable selection      128
Constrained cumulative logit model      297
Contingency table      92—93
Continuation-ratio logistic model      290 295—298
Continuous covariates: goodness-of-fit      175—176
Continuous covariates: variable selection      93—94 103 126
Continuous independent variable: fitted logistic regression      63—64 67 97
Continuous independent variable: variable selection      97
Continuous variables: defined      22
Continuous variables: independent      See Continuous independent variable
Continuous variables: variable selection      93
Coronary heart disease (CHD) study: fitted logistic regression      51—53 56—57 64 71—72
Coronary heart disease (CHD) study: logistic regression      2—7
Correlated data analysis: duster-speci fie      310—312 316—317 320—328
Correlated data analysis: population average model      311—323 329—330
Correlated data analysis: subject-specific      310 312
Correlated data analysis: transitional model      312
Covariance matrix: case-control studies      206—210
Covariance matrix: correlated data analysis      315
Covariance matrix: fitted logistic regression      78
Covariance matrix: logistic regression      19
Covariance matrix: multiple logistic regression      34 41—43
Covariate pattern: defined      144
Covariate pattern: diagnostics and      169 172—183
Covariate pattern: goodness-of-fit assessment      178—179 182 282—287
Covariate pattern: model-building strategies      138
Cox model      205 331—332
Data sets: ICU study      23—25
Data sets: low birth weight study      25
Data sets: prostate cancer study      25—26
Data sets: UMARU IMPACT study      26—28
Degrees-of-freedom: complex sample surveys      214
Degrees-of-freedom: correlated data analysis      328
Degrees-of-freedom: exact computation methods      338
Degrees-of-freedom: fitted linear regression      72 82—83 85
Degrees-of-freedom: goodness-of-fit assessment      154
Degrees-of-freedom: multinomial logistic regression      275
Degrees-of-freedom: multiple logistic regression      38—39
Degrees-of-freedom: ordinal logistic regression model      295 304
Degrees-of-freedom: stepwise logistic regression      116 120
Degrees-of-freedom: variable selection and      92 102 116
Dependent outcome      1
Design matrix      168
Design variables: fitted logistic regression      60—61
Design variables: multiple logistic regression      32 38
Deviance, Pearson      145—147 152—154 179
Deviation from mean coding      59
Deviation from means      54
Diagnostics: basic building blocks      176—178
Diagnostics: coefficient estimation      182
Diagnostics: confounding      185
Diagnostics: correlated data analysis      325—326
Diagnostics: covariate patterns      172—183
Diagnostics: design matrix      168—169
Diagnostics: distribution theory      175
Diagnostics: leverage values      169—172 177
Diagnostics: maximum likelihood estimate (MLE)      184—185
Diagnostics: multinomial logistic regression model      280—287
Diagnostics: Pearson chi-square statistic      174
Diagnostics: residual sum-of-square      167—168
Diagnostics: residuals      178—179
Diagnostics: UIS case study      184
Dichotomous covariate      339—340
Dichotomous independent variable, fitted logistic regression      48—56
Dichotomous logistic regression      1 43
Discrete choice model      260
Discrete variables      22 33
Discriminant analysis      21 138
Discriminant function: analysis      See Discriminant function analysis
Discriminant function: multiple logistic regression      43—44
Discrimination, goodness-of-fit assessment      160 163
Distribution functions      5—6
Due regression sum-of-squares      12
Dummy variables      32
Effect modifier      70
EGRET      85 152 326—327
Error: estimated standard      138—139
Error: fitted logistic regression      58
Error: logistic regression      6—7
Error: multiple logistic regression      34 42
Estimation methods: logistic regression models      21—23
Estimation methods: multinomial logistic regression      264—273
Events per parameter      346
Exchangeable correlation matrix      314

Exchangeable correlation, correlated data analysis      313
Explanatory variables      1
External validation, goodness-of-fit      186—188
Extrabinomial variation      185
F-distribution      213—214
F-test      116
Fisher's Exact Test      334
Fit assessment: 1—1 matched study      236—243
Fit assessment: 1—M matched study      248—259
Fit assessment: exercises      200—202
Fit assessment: external validation      186—118
Fit assessment: logistic regression diagnostics      167—186
Fit assessment: results, interpretation and presentation of      188—200
Fit assessment: summary measures of goodness-of-fit      See Goodness-of-fit assessment factors
Fitted logistic regression model, interpretation of: $2\times2$ tables, stratified analysis compared with      79—85
Fitted logistic regression model, interpretation of: confounding      70—74
Fitted logistic regression model, interpretation of: continuous independent variable      63—64
Fitted logistic regression model, interpretation of: dichotomous independent variable      48—56
Fitted logistic regression model, interpretation of: exercises      88—90
Fitted logistic regression model, interpretation of: fitted values      85—88
Fitted logistic regression model, interpretation of: interaction      70—74
Fitted logistic regression model, interpretation of: link function      48
Fitted logistic regression model, interpretation of: multivariable model      64—69
Fitted logistic regression model, interpretation of: odds ratio, estimation in presence of interaction      74—79
Fitted logistic regression model, interpretation of: polychotomous independent variable      56—72
Fitted values, fitted logistic regression      85—88
Fitting: assessment of      See Fit assessment; Goodness-of-fit assessment
Fitting: correlated data analysis      320 326—330
Fitting: multinomial logistic regression      279—287
Fitting: ordinal logistic regression model      291—292
Fitting: stepwise logistic regression      117—120
Fractional polynomials, variable selection      100—103 109 111
Furnival — Wilson algorithm      128
GEE (generalized estimating equations)      312—316
Generalized additive model, variable selection      103—104
Goodness-of-fit assessment factors: classification tables      156—160 188
Goodness-of-fit assessment factors: Hosmer — Lemeshow tests      147—156 327 338
Goodness-of-fit assessment factors: interaction      188—189
Goodness-of-fit assessment factors: interpretation of      164 183—184
Goodness-of-fit assessment factors: Pearson chi-square statistic and deviance      145—147 152—154 181 218 327
Goodness-of-fit assessment factors: Pearson correlation coefficient      164—165
Goodness-of-fit assessment factors: ROC Curve, area under      160—164
Goodness-of-fit: assessment of      See Goodness-of-fit assessment factors
Goodness-of-fit: defined      143
Goodness-of-fit: fitted logistic regression      85
Goodness-of-fit: logistic regression, generally      11 13
Goodness-of-fit: sample size issues      339—347
Grouping, goodness-of-fit      176
Hat matrix      168
Homogeneity test      82—83
Hosmer — Lemeshow tests      147—156 187 327 338
ICU study      23—25
Identity function      47
Independent model, correlated data analysis      313
Independent variables: continuous      63—69
Independent variables: dichotomous      48—56
Independent variables: fitted logistic regression      47 54
Independent variables: logistic regression      1—2 6—7 14
Independent variables: polychotomous      56—62
Information sandwich estimator      315
Interaction: best subsets linear regression      136—137
Interaction: defined      69
Interaction: fitted logistic regression      70—74 98
Interaction: goodness-of-fit assessment      188—189
Interaction: stepwise logistic regression      125—128
Interaction: variable selection      98—99
Intercept coefficient      47 135
Least squares: logistic regression      7—8
Least squares: multiple logistic regression      43
Leverage values, goodness-of-fit assessment      169—172 177
Likelihood equations      8 33
Likelihood function: logistic regression model, generally      8
Likelihood function: multinomial logic regression      262
Likelihood function: multiple logistic regression      33
Likelihood function: sampling models      206 209 212
Likelihood ratio test: correlated data analysis      321
Likelihood ratio test: goodness-of-fit assessment      146
Likelihood ratio test: logistic regression      13 15—16
Likelihood ratio test: multiple logistic regression      37
Likelihood ratio test: variable selection      97 120
Likelihood ratio: defined      13
Likelihood ratio: multinomial logistic regression      276—277
Likelihood ratio: ordinal logistic regression model      305—307
Likelihood ratio: stepwise linear regression      117
Likelihood ratio: test      See Likelihood ratio test
Likelihood ratio: variable selection and      92 117
Limits, fitted logistic regression      59
Linear regression model, logistic distinguished from with      1 6—7
Link function, fitted logistic regression      47—48
Log likelihood function: best subsets linear regression      123
Log likelihood function: case-control studies      211
Log likelihood function: correlated data analysis      316
Log likelihood function: logistic regression model, generally      8 15
Log likelihood function: multinomial logistic regression      270
Log likelihood function: multiple logistic regression      34
Log-odds ratio: fitted linear regression      63—64 67—68 75—76 79
Log-odds ratio: linear regression      18
Logistic distribution, generally      6
Logistic regression model: coefficients, testing for significance of      11—17
Logistic regression model: confidence interval estimation      17—23
Logistic regression model: data sets      23—28
Logistic regression model: estimation methods      21—23
Logistic regression model: exact methods for      330—339
Logistic regression model: example of      2—7
Logistic regression model: exercises      29—30
Logistic regression model: fitting      7—10
Logistic regression model: interpretation of      See Fitted logistic regression model
Logistic regression model: model-building strategies      See Model-building strategies
Logistic regression model: purpose of      1
Logistic regression model: sample size issues      339—347
Logit: fitted logistic regression      48 67 70—71 73—75
Logit: logistic regression      17—19
Logit: multiple logistic regression      31—32 40 42
Logit: transformation      6 48
Logit: variable selection      97
LogXact 4      331 334 338
Low birth weight study: correlated data analysis      318—330
Low birth weight study: fitted linear regression      77 80 86—88
Low birth weight study: logistic regression      25
Low birth weight study: matched case-control study      230—243
Low birth weight study: multiple logistic regression      35—38
Low birth weight study: ordinal logistic regression model      292—308
m-asymptotics      145 147 150 175—176 187 210
Main effects model      98
Mammography experience study      265—287
Mantel — Haenszel estimator      79—80 82—83 85
Matched case-control studies      1—M matched study
Matched case-control studies, characteristics of      223—226
Matrix notation, best subsets logistic regression      128—129. See also Specific types of matrices
Maximum likelihood estimation (MLE): best subsets linear regression      128 130—131
Maximum likelihood estimation (MLE): case-control studies      208 226
Maximum likelihood estimation (MLE): fitted logistic regression      63 84
Maximum likelihood estimation (MLE): goodness-of-fit assessment      173 184
Maximum likelihood estimation (MLE): logistic regression      8—10 23
Maximum likelihood estimation (MLE): matched case-control studies      226—227
Maximum likelihood estimation (MLE): multinomial logistic regression      263
Maximum likelihood estimation (MLE): multiple logistic regression      33
Maximum likelihood estimation (MLE): ordinal logistic regression models      291
Maximum likelihood estimation (MLE): stepwise logistic regression      121
Maximum likelihood estimation (MLE): variable selection      100
Median unbiased estimator (MUE)      337
Model-building strategies: best subsets      128—135
Model-building strategies: covariates      138
Model-building strategies: exercises      142
Model-building strategies: fitting      140
Model-building strategies: numerical problems      135—141
Model-building strategies: overfitting      135—136
Model-building strategies: pooling      136—137
Model-building strategies: stepwise logistic regression      116—128
Model-building strategies: variable selection      92—116

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