The Multivariate Social Scientist; Introductory Statistics Using Generalized Linear Models

by Graeme D Hutcheson

• ISBN13: 9780761952015
• ISBN10: 0761952012
• eBook ISBN(s): 9781446229941
• Format: Paperback
• Copyright: 1999-07-06
• Publisher: Sage Publications Ltd
• More Book Details

Summary

Starting from simple hypothesis testing and then moving towards model-building, this valuable book takes readers through the basics of multivariate analysis including: which tests to use on which data; how to run analyses in SPSS for Windows and GLIM4; how to interpret results; and how to report and present the reports appropriately.Using a unified conceptual framework (based around the Generalized Linear Model) the authors explain the commonalities and relationships between methods that include both the analysis of categorical and continuous data.

Table of Contents

Preface	xi
Introduction	1	(14)
Generalized Linear Models	2	(3)
The Random Component	3	(1)
The Systematic Component	3	(1)
The Link Function	4	(1)
Data Formats	5	(1)
Standard Statistical Analyses within the GLM Framework	6	(1)
Goodness-of-fit Measures and Model-Building	7	(2)
The Analysis of Deviance	9	(1)
Assumptions of GLMs	10	(3)
Properties of Scales and Corresponding Transformations	10	(1)
Overdispersion and the Variance Function	11	(1)
Non-linearity and the Link Function	12	(1)
Independent Measurement	12	(1)
Extrapolating Beyond the Measured Range of Variates	13	(1)
Summary	13	(2)
Data Screening	15	(40)
Levels of Measurement	16	(1)
Data Accuracy	17	(1)
Reliable Correlations	17	(1)
Missing Data	18	(1)
Outliers	19	(6)
On a Single Variable	20	(1)
Across Multiple Variables	20	(1)
Identifying Outliers	21	(1)
Leverage Values	21	(1)
Cook's Distance	22	(2)
Dealing with Outliers	24	(1)
Using Residuals to Check for Violations of Assumptions	25	(1)
Ordinary Residuals	26	(1)
Standardized Residuals	26	(1)
Studentized Residuals	26	(1)
Assumptions	26	(5)
Normality	26	(2)
Constant Variance	28	(1)
Linearity	29	(2)
Independence	31	(1)
Transformation and Curvilinear Models	31	(10)
Box--Cox Transformation with Skewed Errors	32	(3)
Fitting Models to Curvilinear Data Trends	35	(6)
Multicollinearity and Singularity	41	(1)
Diagnostics for Logistic Regression and Loglinear Models	42	(2)
Under and Overdispersion	42	(2)
Summary and Recommendations on the Order of Screening Practices	44	(1)
Statistical Software Commands	45	(10)
SPSS	45	(4)
GLIM	49	(6)
Ordinary Least-Squares Regression	55	(58)
Simple OLS Regression	56	(12)
The Regression Equation	56	(3)
Confidence Intervals for β	59	(3)
Confidence Intervals for Fitted y	62	(1)
Prediction Intervals	63	(2)
Goodness-of-fit Measures	65	(1)
The R2 Statistic	65	(1)
The F Statistic	66	(2)
A Worked Example of Simple Regression	68	(3)
Multiple OLS Regression	71	(27)
The Regression Equation	73	(1)
Interactions and Curvilinearity	73	(2)
Confidence Intervals for β	75	(1)
Confidence Intervals for Fitted y	75	(1)
Prediction Intervals	75	(1)
Goodness-of-fit Measures	76	(1)
The R2 and R2a Statistics	76	(1)
The F and Partial-F Statistics	77	(1)
Multicollinearity	78	(1)
Perfect Multicollinearity	79	(1)
High Multicollinearity	80	(2)
Identifying Instances of Multicollinearity	82	(2)
Dealing with Multicollinearity	84	(1)
Dummy Variable Coding Discontinuous Data	85	(1)
Indicator Coding	86	(4)
Deviation Coding	90	(3)
Dummy Coding Ordered Categorical Data	93	(1)
Model Selection	94	(1)
Criteria for Including and Removing Variables	94	(1)
Automated Model Selection	95	(1)
Forward Selection	96	(1)
Backward Elimination	97	(1)
Stepwise Selection	97	(1)
A Worked Example of Multiple Regression	98	(3)
Summary	101	(1)
Statistical Software Commands	102	(11)
SPSS	102	(4)
GLIM	106	(7)
Logistic Regression	113	(50)
Simple Logistic Regression	114	(16)
The Regression Equation	117	(4)
Calculating and Interpreting Model Parameters	121	(2)
Confidence Intervals for β	123	(1)
Confidence Intervals for Fitted y	124	(3)
Under and Overdispersion	127	(1)
Goodness-of-fit Measures	128	(1)
The Log-Likelihood Statistic	128	(1)
The Wald Statistic	129	(1)
Analysis of Classification Table Data	129	(1)
A Worked Example of Simple Logistic Regression	130	(4)
Multiple Logistic Regression	134	(13)
The Regression Equation	134	(1)
Interactions and Curvilinearity	135	(1)
Calculating and Interpreting Model Parameters	136	(1)
Confidence Intervals for β	137	(1)
Confidence Intervals for Fitted y	138	(1)
Goodness-of-fit Measures	139	(1)
The Log-Likelihood Statistic	139	(2)
Multicollinearity	141	(1)
Dummy Variable Coding Discontinuous Data	141	(2)
Indicator Coding	143	(1)
Deviation Coding	144	(1)
Model Selection	145	(1)
Criteria for Including and Removing Variables	146	(1)
A Worked Example of Multiple Logistic Regression	147	(5)
Summary	152	(1)
Statistical Software Commands	152	(11)
SPSS	152	(4)
GLIM	156	(7)
Loglinear Analysis	163	(54)
Traditional Bivariate Methods	164	(6)
Hypothesis Testing with Significance Tests	164	(1)
Goodness-of-fit Statistics	165	(1)
The Pearson X2 Statistic	165	(1)
The G2 Statistic	166	(1)
Adjusted Residuals	167	(1)
Modelling with Sample Odds Ratios	168	(1)
Confidence Intervals	169	(1)
Loglinear Models	170	(29)
The Loglinear Equation	171	(1)
A Bivariate Example	172	(3)
A Multivariate Example	175	(1)
Model Notation	175	(2)
Model Building	177	(2)
Goodness-of-fit Statistics and Residuals	179	(3)
Explanatory Variables with Ordered Categories	182	(1)
Scoring Ordered Categorical Variables	183	(1)
Bivariate Example with Explanatory Variables having Ordered Categories	184	(2)
Associations Between Nominal and Ordered Categorical Variables	186	(3)
Homogeneous Linear x Linear Associations	189	(2)
Logit Analysis --- Evaluating a Binary Response Variable	191	(1)
Multicategory Response Variables with Nominal and Ordered Categories	192	(1)
Nominal Response Variables: Baseline Category Logits	192	(1)
Ordered Response Variables	193	(6)
Summary	199	(1)
Statistical Software Commands	200	(17)
SPSS	200	(5)
GLIM	205	(12)
Factor Analysis	217	(36)
Overview	218	(2)
Factor Analysis Equations	220	(1)
Preliminary Analyses	221	(5)
Data Assumptions	222	(1)
Continuous and Ordered Categorical Data	222	(1)
Sample Size	222	(1)
Data Screening	222	(1)
Examining Correlations	223	(1)
Measures of Sampling Adequacy	224	(2)
Factor Extraction	226	(6)
Principal Components Analysis	226	(2)
Selecting the Number of Factors	228	(2)
Interpreting the Initial Factors	230	(2)
Factor Rotation	232	(5)
Interpreting the Rotated Factors	235	(2)
Including Factors in GLMs	237	(1)
A Worked Example of Factor Analysis	238	(10)
Summary	248	(1)
Statistical Software Commands	248	(5)
SPSS	249	(4)
Conclusion	253	(14)
Main Points of the GLM Framework	253	(1)
Sampling Assumptions and GLMs	254	(1)
Measurement Assumptions of Explanatory Variables in GLMs	255	(1)
Ordinal Variables	256	(1)
GLM Variants of ANOVA and ANCOVA	257	(1)
Repeated Measurements	258	(1)
Time Series Analysis	259	(1)
Gamma Errors and the Link Function: an Alternative to Data Transformation	260	(1)
Survival Analysis	261	(1)
Exact Sample and Sparse Data Methods	262	(1)
Cross Validation of Models	263	(1)
Software Recommendations	263	(4)
SPSS for Windows	263	(1)
GLIM	264	(1)
SAS	264	(1)
GENSTAT for Windows	264	(1)
Overall	265	(2)
References	267	(7)
Index	274