Checking Normality and Homoscedasticity in the General Linear Model Using Diagnostic Plots

Inference for the general linear model makes several assumptions, including independence of errors, normality, and homogeneity of variance. Departure from the latter two of these assumptions may indicate the need for data transformation or removal of outlying observations. Informal procedures such a...

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Veröffentlicht in:Communications in statistics. Simulation and computation Jg. 41; H. 2; S. 141 - 154
Hauptverfasser: Schützenmeister, A., Jensen, U., Piepho, H.-P.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Colchester Taylor & Francis Group 01.02.2012
Taylor & Francis
Taylor & Francis Ltd
Schlagworte:
62-09
62J5
Approximation
Computer simulation
Constant residual variance
Correlation
Diagnostic systems
Distribution theory
Exact sciences and technology
Homogeneity
Linear inference, regression
Mathematics
Model checking
Monte Carlo
Multiplicity
Multivariate analysis
Normality
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Probability and statistics
Residual plot
Sciences and techniques of general use
Simulation
Simultaneous tolerance band
Statistics
Tolerance interval
Tolerance region
Tolerances
Transformations
Correlation
Generalized linear model
Statistical distribution
Error estimation
Data transformation
Gaussian distribution
Non parametric estimation
Multivariate analysis
Stochastic method
Constant residual variance
Linear model
Variance
Tolerance interval
Outlier
Statistical test
Monte Carlo
Multiplicity
Model checking
Approximation theory
62F25
Monte Carlo method
Discriminant analysis
Covariance analysis
Independence
Probability
Tolerance
Statistical association
Statistical estimation
Algorithm
Variance analysis
Heteroscedasticity
Confidence interval
Statistical method
Statistical regression
Diagnostic techniques
Residual plot
Numerical analysis
Non normality
Simulation
Simultaneous tolerance band
Correlation analysis
Tolerance region
Normality test
Numerical simulation
Computing method
ISSN:0361-0918, 1532-4141
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Beschreibung
Zusammenfassung:Inference for the general linear model makes several assumptions, including independence of errors, normality, and homogeneity of variance. Departure from the latter two of these assumptions may indicate the need for data transformation or removal of outlying observations. Informal procedures such as diagnostic plots of residuals are frequently used to assess the validity of these assumptions or to identify possible outliers. A simulation-based approach is proposed, which facilitates the interpretation of various diagnostic plots by adding simultaneous tolerance bounds. Several tests exist for normality or homoscedasticity in simple random samples. These tests are often applied to residuals from a linear model fit. The resulting procedures are approximate in that correlation among residuals is ignored. The simulation-based approach accounts for the correlation structure of residuals in the linear model and allows simultaneously checking for possible outliers, non normality, and heteroscedasticity, and it does not rely on formal testing. [Supplementary materials are available for this article. Go to the publisher's online edition of Communications in Statistics-Simulation and Computation ® for the following three supplemental resource: a word file containing figures illustrating the mode of operation for the bisectional algorithm, QQ-plots, and a residual plot for the mussels data.]
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ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2011.582560