Unifying Political Methodology : The Likelihood Theory of Statistical Inference

Preface xi I Theory 3(94) 1 Introduction 3(11) 1.1 Toward a new political methodology 3(3) 1.2 A language of inference 6(7) 1.3 Concluding remarks 13(1) 2 Conceptualizing uncertainty and inference 14(24) 2.1 Probability as a model of uncertainty 14(2) 2.2 Inverse probability as a failed model of inference 16(5) 2.3 Likelihood as a model of inference 21(7) 2.4 The Bayesian model of inference 28(2) 2.5 Restrictive versus unrestrictive statistical models 30(5) 2.6 Specification tests 35(1) 2.7 Concluding remarks 36(2) 3 The probability model of uncertainty 38(21) 3.1 The probability model 38(3) 3.2 Univariate probability distributions 41(16) Bernoulli distribution 42(1) Binomial distribution 43(2) Extended beta-binomial distribution 45(3) Poisson distribution 48(3) Negative binomial distribution 51(2) Normal distribution 53(1) Log-Normal distribution 54(2) Where derivation from first principles is difficult or indeterminate 56(1) 3.3 Multivariate probability distributions 57(1) 3.4 Concluding remarks 58(1) 4 The likelihood model of inference 59(38) 4.1 Likelihood and summary estimation 59(7) 4.2 Likelihood and point estimation 66(7) Analytical methods 67(5) Numerical methods 72(1) 4.3 An alternative representation of the likelihood function 73(1) 4.4 Properties of maximum likelihood estimators 74(7) Regularity conditions 74(1) Finite sample properties 75(2) Asymptotic properties 77(4) 4.5 Problems to avoid with maximum likelihood estimators 81(2) 4.6 Precision of maximum likelihood estimators 83(9) Likelihood ratio test 84(3) Direct measures of precision 87(3) Wald's test 90(2) 4.7 Likelihood and interval estimation 92(1) 4.8 Concluding remarks 93(4) II Methods 97(158) 5 Discrete regression models 97(36) 5.1 Binary variables 98(4) 5.2 Interpreting functional forms 102(8) Graphical methods 104(2) Fitted values 106(1) First differences 107(1) Derivative methods 108(2) 5.3 Alternative justifications for binary variable models 110(5) Threshold models 110(3) Utility maximization models 113(1) First principles of first principles 114(1) 5.4 Ordered categorical variables 115(2) 5.5 Grouped uncorrelated binary variables 117(2) 5.6 Grouped correlated binary variables 119(2) 5.7 Counts of uncorrelated events 121(3) 5.8 Counts of uncorrelated events with unequal observation intervals 124(2) 5.9 Counts of correlated events 126(5) 5.10 Concluding remarks 131(2) 6 Models for tabular data 133(29) 6.1 Notation 135(1) 6.2 The log-odds (logit) model 136(7) 6.3 A specification test 143(3) 6.4 The log-proportion model 146(3) 6.5 The linear-proportion model 149(3) 6.6 The log-frequency (log-linear) model 152(6) 6.7 The log-odds model as a special case of the log-frequency model 158(2) 6.8 Concluding remarks 160(2) 7 Time series models 162(27) 7.1 Stochastic explanatory variables 165(2) 7.2 The influence of history 167(9) Exogenous variables 169(1) Past expectations 170(3) Past realizations 173(1) Past shocks 173(3) Combinations 176(1) 7.3 Theoretical ambiguities 176(5) 7.4 The first differences error correction model 181(4) 7.5 The "standard" time series regression model 185(2) 7.6 Concluding remarks 187(2) 8 Introduction to multiple equation models 189(19) 8.1 Identification 191(6) Example 1: Flat likelihoods 192(1) Example 2: Nonunique reparameterization 193(1) Example 3: Deterministic relationships among the ML estimators 194(2) What to do 196(1) 8.2 Reciprocal causation 197(4) A linear model 198(3) 8.3 Poisson regression models with unobserved dependent variables 201(6) 8.4 Concluding remarks 207(1) 9 Models with nonrandom selection 208(23) 9.1 Censoring 208(2) 9.2 Stochastic censoring 210(3) 9.3 Stochastic truncation 213(3) 9.4 Truncated and variance function event count models 216(6) A truncated negative binomial model 218(3) Truncated negative binomial with variance function 221(1) 9.5 Hurdle event count models 222(7) 9.6 Concluding remarks 229(2) 10 General classes of multiple equation models 231(19) 10.1 Factor analysis 231(4) 10.2 Analyzing covariance structures 235(3) 10.3 A specification test 238(1) 10.4 A general linear structural equation model 239(9) The general model 240(2) The likelihood function 242(2) Special cases 244(3) General comments 247(1) 10.5 Concluding remarks 248(2) 11 Conclusions 250(5) References 255(14) Index 269