MODEL SELECTION AND MODEL AVERAGING

By LINDA ANDERSON

CONTENTS MODEL SELECTION: DATA EXAMPLES AND INTRODUCTION INTRODUCTION EGYPTIAN SKULL DEVELOPMENT WHO WROTE ‘THE QUIET DON’? SURVIVAL DATA ON PRIMARY BILIARY CIRRHOSIS LOW BIRTHWEIGHT DATA FOOTBALL MATCH PREDICTION SPEEDSKATING PREVIEW OF THE FOLLOWING CHAPTERS NOTES ON THE LITERATURE AKAIKE’S INFORMATION CRITERION INFORMATION CRITERIA FOR BALANCING ?T WITH COMPLEXITY MAXIMUM LIKELIHOOD AND THE KULLBACK–LEIBLER DISTANCE AIC AND THE KULLBACK–LEIBLER DISTANCE EXAMPLES AND ILLUSTRATIONS TAKEUCHI’S MODEL-ROBUST INFORMATION CRITERION CORRECTED AIC FOR LINEAR REGRESSION AND AUTOREGRESSIVE TIME SERIES AIC, CORRECTED AIC AND BOOTSTRAP-AIC FOR GENERALISED LINEAR MODELS? BEHAVIOUR OF AIC FOR MODERATELY MISSPECI?ED MODELS? CROSS-VALIDATION OUTLIER-ROBUST METHODS EXERCISES THE BAYESIAN INFORMATION CRITERION EXAMPLES AND ILLUSTRATIONS OF THE BIC DERIVATION OF THE BIC THE BIC AND AIC FOR HAZARD REGRESSION MODELS THE DEVIANCE INFORMATION CRITERION MINIMUM DESCRIPTION LENGTH A COMPARISON OF SOME SELECTION METHODS COMPARING SELECTORS: CONSISTENCY, EF?CIENCY AND PARSIMONY PROTOTYPE EXAMPLE: CHOOSING BETWEEN TWO NORMAL MODELS STRONG CONSISTENCY AND THE HANNAN–QUINN CRITERION MALLOWS’S C P AND ITS OUTLIER-ROBUST VERSIONS EF?CIENCY OF A CRITERION EF?CIENT ORDER SELECTION IN AN AUTOREGRESSIVE PROCESS AND THE FPE EF?CIENT SELECTION OF REGRESSION VARIABLES RATES OF CONVERGENCE? TAKING THE BEST OF BOTH WORLDS?? BIGGER IS NOT ALWAYS BETTER SOME CONCRETE EXAMPLES LARGE-SAMPLE FRAMEWORK FOR THE PROBLEM A PRECISE TOLERANCE LIMIT TOLERANCE REGIONS AROUND PARAMETRIC MODELS COMPUTING TOLERANCE THRESHOLDS AND RADII HOW THE 5000-M TIME IN?UENCES THE 10,000-M TIME LARGE-SAMPLE CALCULUS FOR AIC THE FOCUSSED INFORMATION CRITERION ESTIMATORS AND NOTATION IN SUBMODELS THE FOCUSSED INFORMATION CRITERION, FIC LIMIT DISTRIBUTIONS AND MEAN SQUARED ERRORS IN SUBMODELS A BIAS-MODI?ED FIC CALCULATION OF THE FIC ILLUSTRATIONS AND APPLICATIONS EXACT MEAN SQUARED ERROR CALCULATIONS FOR LINEAR REGRESSION? THE FIC FOR COX PROPORTIONAL HAZARD REGRESSION MODELS AVERAGE-FIC A BAYESIAN FOCUSSED INFORMATION CRITERION? FREQUENTIST AND BAYESIAN MODEL AVERAGING ESTIMATORS-POST-SELECTION SMOOTH AIC, SMOOTH BIC AND SMOOTH FIC WEIGHTS DISTRIBUTION OF MODEL AVERAGE ESTIMATORS WHAT GOES WRONG WHEN WE IGNORE MODEL SELECTION? BETTER CON?DENCE INTERVALS SHRINKAGE, RIDGE ESTIMATION AND THRESHOLDING BAYESIAN MODEL AVERAGING A FREQUENTIST VIEW OF BAYESIAN MODEL AVERAGING? BAYESIAN MODEL SELECTION WITH CANONICAL NORMAL PRIORS? LACK-OF-?T AND GOODNESS-OF-?T TESTS THE PRINCIPLE OF ORDER SELECTION ASYMPTOTIC DISTRIBUTION OF THE ORDER SELECTION TEST THE PROBABILITY OF OVER?TTING? SCORE-BASED TESTS TWO OR MORE COVARIATES NEYMAN’S SMOOTH TESTS AND GENERALISATIONS A COMPARISON BETWEEN AIC AND THE BIC FOR MODEL TESTING? GOODNESS-OF-?T MONITORING PROCESSES FOR REGRESSION MODELS? MODEL SELECTION AND AVERAGING SCHEMES IN ACTION AIC AND BIC SELECTION FOR EGYPTIAN SKULL DEVELOPMENT DATA LOW BIRTHWEIGHT DATA: FIC PLOTS AND FIC SELECTION PER STRATUM SURVIVAL DATA ON PBC: FIC PLOTS AND FIC SELECTION SPEEDSKATING DATA: AVERAGING OVER COVARIANCE STRUCTURE MODELS FURTHER TOPICS MODEL SELECTION IN MIXED MODELS BOUNDARY PARAMETERS FINITE-SAMPLE CORRECTIONS? MODEL SELECTION WITH MISSING DATA WHEN P AND Q GROW WITH N OVERVIEW OF DATA EXAMPLES REFERENCES