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A theme running through this book is that of making inference about sources of variation or uncertainty, and the author shows how information about these sources can be used for improved estimation of certain elementary quantities. Amongst the topics covered are: essay rating, summarizing item-level properties, equating of tests, small-area estimation, and incomplete longitudinal studies. Throughout, examples are given using real data sets which exemplify these applications.
1 Inference about variation.- 1.1 Imperfection and variation.- 1.2 Educational measurement and testing.- 1.3 Statistical context.- 1.3.1 Statistical objects.- 1.3.2 Estimation.- 1.3.3 Correlation structure and similarity.- 1.3.4 Notation.- 2 Reliability of essay rating.- 2.1 Introduction.- 2.2 Models.- 2.3 Estimation.- 2.4 Extensions.- 2.5 Diagnostic procedures.- 2.6 Examples.- 2.6.1 Advanced Placement tests.- 2.7 Standard errors.- 2.7.1 Simulations.- 2.8 Summary.- 2.9 Literature review.- 3 Adjusting subjectively rated scores.- 3.1 Introduction.- 3.2 Estimating severity.- 3.3 Examinee-specific shrinkage.- 3.3.1 Rating in a single session.- 3.3.2 Shrinking to the rater s mean.- 3.4 General scheme.- 3.4.1 Sensitivity and robustness.- 3.5 More diagnostics.- 3.6 Examples.- 3.6.1 Advanced Placement tests.- 3.7 Estimating linear combinations of true scores.- 3.7.1 Optimal linear combinations.- 3.8 Summary.- Appendix. Derivation of MSE for the general adjustment scheme.- 4 Rating several essays.- 4.1 Introduction.- 4.2 Models.- 4.3 Estimation.- 4.4 Application.- 4.4.1 Itemwise analyses.- 4.4.2 Simultaneous analysis.- 4.5 Choice of essay topics.- 4.5.1 Modelling choice.- 4.5.2 Simulations.- 4.6 Summary.- 5 Summarizing item-level properties.- 5.1 Introduction.- 5.2 Differential item functioning.- 5.3 DIF variance.- 5.4 Estimation.- 5.5 Examples.- 5.5.1 National Teachers Examination.- 5.5.2 GRE Verbal test.- 5.6 Shrinkage estimation of DIF coefficients.- 5.7 Model criticism and diagnostics.- 5.8 Multiple administrations.- 5.8.1 Estimation.- 5.8.2 Examples.- 5.8.3 Other applications.- 5.9 Conclusion.- 6 Equating and equivalence of tests.- 6.1 Introduction.- 6.2 Equivalent scores.- 6.2.1 Equating test forms.- 6.2.2 Half-forms.- 6.2.3 Linear true-score equating.- 6.3 Estimation.- 6.4 Application.- 6.4.1 Data and analysis.- 6.4.2 Comparing validity.- 6.4.3 Model criticism.- 6.5 Summary.- 7 Inference from surveys with complex sampling design.- 7.1 Introduction.- 7.2 Sampling design.- 7.2.1 The realized sampling design.- 7.2.2 The model sampling design.- 7.2.3 Sampling weights and non-response.- 7.3 Proficiency scores.- 7.3.1 Imputed values.- 7.4 Jackknife.- 7.5 Model-based method.- 7.5.1 Stratification and clustering.- 7.5.2 Sampling variance of the ratio estimator.- 7.5.3 Within-cluster variance.- 7.5.4 Between-cluster variance.- 7.5.5 Multivariate outcomes.- 7.6 Examples.- 7.6.1 Subpopulation means.- 7.6.2 How much do weights matter?.- 7.7 Estimating proportions.- 7.7.1 Percentiles.- 7.8 Regression with survey data.- 7.9 Estimating many subpopulation means.- 7.10 Jackknife and model-based estimators.- 7.11 Summary.- 8 Small-area estimation.- 8.1 Introduction.- 8.2 Shrinkage estimation.- 8.3 Regression with survey data.- 8.4 Fitting two-level regression.- 8.4.1 Restricted maximum likelihood.- 8.4.2 Sampling weights.- 8.5 Small-area mean prediction.- 8.6 Selection of covariates.- 8.7 Application.- 8.7.1 No adjustment.- 8.7.2 Adjustment for covariates.- 8.7.3 Prediction and cross-validation.- 8.7.4 Refinement.- 8.8 Summary and literature review.- 9 Cut scores for pass/fail decisions.- 9.1 Introduction.- 9.2 Models.- 9.3 Fitting logistic regression.- 9.3.1 Generalized linear models.- 9.3.2 Random coefficients.- 9.3.3 Cut score estimation.- 9.4 Examples.- 9.4.1 PPST Writing test.- 9.4.2 Physical Education.- 9.5 Summary.- 10 Incomplete longitudinal data.- 10.1 Introduction.- 10.2 Informative missingness.- 10.3 Longitudinal analysis.- 10.4 EM algorithm.- 10.5 Application.- 10.6 Estimation.- 10.6.1 Variation in growth.- 10.6.2 Covariate adjustment.- 10.6.3 Missing covariate data.- 10.6.4 Standard errors.- 10.6.5 Clustering.- 10.7 Summary.- References.
