THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

Estimation and Inference in Econometrics

Statistical Analysis with Missing Data

Statistical Analysis With Missing Data (2nd ed.) (Book)

The coefficient of determination R2 quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R2 for g...

https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2017.0213

The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded.

Measuring the proportion of variance explained (R2) by a statistical model and the relative importance of specific predictors (semi-partial R2) can be essential considerations when building a parsimonious statistical model. The R2 statistic is a familiar summary of goodness-of-fit for normal linear models and has been extended in various ways to more general models. In particular, the generalized linear mixed model (GLMM) extends the normal linear model and is used to analyze correlated (hierarchical), non-normal data structures. Although various R2 statistics have been proposed, there is no consensus in statistical literature for the most sensible definition of R2 in this context. This research aims to build upon existing knowledge and definitions of R2 and to concisely define the statistic for the GLMM. Here, we derive a model and semi-partial R2 statistic for fixed (population) effects in the GLMM by utilizing the penalized quasi-likelihood estimation method based on linearization. We show that...

An R2 statistic for fixed effects in the generalized linear mixed model

The term “empirical predictor” refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML estimators are used for the second stage. We obtain second-order approximation to the MSE as well as an estimator of the MSE correct to the same order. The general results are applied to mixed linear models to obtain a second-order approximation to the MSE of the empirical best linear unbiased predictor (EBLUP) of a linear mixed effect and an estimator of the MSE of EBLUP whose bias is correct to second order. The general mixed linear model includes the mixed ANOVA model and the longitudinal model as special cases.

/pdf/mean-squared-error-of-empirical-predictor-2iqvd14gu5.pdf

Mean squared error of empirical predictor

SUMMARY Liang & Zeger (1986) introduced a generalised estimating equations approach based on a 'working' correlation matrix to obtain consistent and efficient estimators of regression parameters in the class of generalised linear models for repeated measures data. As demonstrated by Crowder (1995), because of the uncertainty of definition of the working correlation matrix, the Liang-Zeger approach may in some cases lead to a complete breakdown of the estimation of the regression parameters. In this paper we show that, even though the Liang-Zeger approach in many situations yields consistent estimators for the regression parameters, these estimators are usually inefficient as compared to the regression estimators obtained by using the independence estimating equations approach.

Miscellanea. On the efficiency of regression estimators in generalised linear models for longitudinal data

We conducted an institutional-based retrospective study on 308 uveitic patients and analyzed the pattern of uveitis in Northeastern India. Anterior uveitis was the most common type (47.07%) followed by posterior (29.87%), intermediate (12.98%) and panuveitis (10.06%). Toxoplasmosis (40.21%) had the highest incidence among posterior uveitis cases. Harada's form of Vogt Koyanagi Harada's disease is a frequent occurrence in this subset of the population.

Pattern of uveitis in North East India: a tertiary eye care center study.

Background: The northeastern region (NER) of India is geographically isolated and ethno-culturally different from the rest of the country. There is lacuna regarding the data on causes of blindness and severe visual impairment in children from this region. Aim: To determine the causes of severe visual impairment and blindness amongst children from schools for the blind in the four states of NER of India. Design and Setting: Survey of children attending special education schools for the blind in the NER. Materials and Methods: Blind and severely visually impaired children (best corrected visual acuity Statistical Analysis: Microsoft Excel Windows software with SPSS. Results: A total of 376 students were examined of whom 258 fulfilled the eligibility criteria. The major anatomical causes of visual loss amongst the 258 were congenital anomalies (anophthalmos, microphthalmos) 93 (36.1%); corneal conditions (scarring, vitamin A deficiency) 94 (36.7%); cataract or aphakia 28 (10.9%), retinal disorders 15 (5.8%) and optic atrophy 14 (5.3%). Nearly half of the children were blind from conditions which were either preventable or treatable (48.5%). Conclusion: Nearly half the childhood blindness in the NER states of India is avoidable and Vitamin A deficiency forms an important component unlike other Indian states. More research and multisectorial effort is needed to tackle congenital anomalies.

/pdf/causes-of-childhood-blindness-in-the-northeastern-states-of-1achzb7n7g.pdf

Kalyan Das

Papers

An R2 statistic for fixed effects in the generalized linear mixed model

Mean squared error of empirical predictor

Miscellanea. On the efficiency of regression estimators in generalised linear models for longitudinal data

Pattern of uveitis in North East India: a tertiary eye care center study.

Causes of childhood blindness in the northeastern states of India