Improved Added Variable and Partial Residual Plots for the Detection of Influential Observations in Generalized Linear Models

Hines, R. J. O′Hara; Carter, E. M.

doi:10.2307/2347405

Cited by 45 publications

(14 citation statements)

References 29 publications

(28 reference statements)

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“…The discreteness of categorical outcomes makes it difficult to interpret such displays. Several authors (Landwehr et al, 1984;Wang, 1985Wang, , 1987O'Hara Hines and Carter, 1993) had developed residuals under the generalized linear model framework, and successfully implemented these residuals in creating diagnostic plots. In marginalizing covariate effects of RLCA, we provided a formula for residuals of categorical responses, which were a "vector"-version extension of previous residuals, and could be applied broadly.…”

Section: Discussionmentioning

confidence: 99%

Selecting the number of classes under latent class regression: a factor analytic analogue

Huang

2005

Psychometrika

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Section: Discussionmentioning

confidence: 99%

Selecting the number of classes under latent class regression: a factor analytic analogue

Huang

2005

Psychometrika

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“…a plot of Y against X 1 while holding the remaining explanatory variables X 2... X k constant) are readily available (Larsen and McCleary 1972, Belsey et al 1980, Velleman and Welsch 1981, Cook and Weisberg 1982, Neter et al 1996, Montgomery et al 2001, and can be very useful for several purposes (below). Although it is beyond the scope of the current paper, plots of partial relationships have also been devised for other types of distribution in generalized linear models (Hines and Carter 1993). These plots depict the true regression coefficient within the multiple regression model as the slope of a fitted line.…”

Section: Plotting Partial Correlation and Regression In Ecological Stmentioning

confidence: 99%

“…However, in simple regression, the fastest way to detect outliers is by displaying a bi-variate scatterplot. Again, both partial plots can also be used to show outliers and influential observations in multiple regression (Larsen and McCleary 1972, Velleman and Welsch 1981, Hines and Carter 1993. Usually plots of residuals versus predicted values are displayed to detect this sort of problem as well as others, such as departures from normality and heteroscedascity of the residuals.…”

Section: Outliers and Influential Data Pointsmentioning

confidence: 99%

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Plotting partial correlation and regression in ecological studies

Moya-Laraño

Corcobado

2008

Web Ecol.

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Multiple regression, the General linear model (GLM) and the Generalized linear model (GLZ) are widely used in ecology. The widespread use of graphs that include fitted regression lines to document patterns in simple linear regression can be easily extended to these multivariate techniques in plots that show the partial relationship of the dependent variable with each independent variable. However, the latter procedure is not nearly as widely used in ecological studies. In fact, a brief review of the recent ecological literature showed that in ca. 20% of the papers the results of multiple regression are displayed by plotting the dependent variable against the raw values of the independent variable. This latter procedure may be misleading because the value of the partial slope may change in magnitude and even in sign relative to the slope obtained in simple least-squares regression. Plots of partial relationships should be used in these situations. Using numerical simulations and real data we show how displaying plots of partial relationships may also be useful for: 1) visualizing the true scatter of points around the partial regression line, and 2) identifying influential observations and non-linear patterns more efficiently than using plots of residuals vs. fitted values. With the aim to help in the assessment of data quality, we show how partial residual plots (residuals from overall model + predicted values from the explanatory variable vs. the explanatory variable) should only be used in restricted situations, and how partial regression plots (residuals of Y on the remaining explanatory variables vs. residuals of the target explanatory variable on the remaining explanatory variables) should be the ones displayed in publications because they accurately reflect the scatter of partial correlations. Similarly, these partial plots can be applied to visualize the effect of continuous variables in GLM and GLZ for normal distributions and identity link functions

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“…Although originally devoted to specific sub-classes of models, these papers introduced ideas that have successively been used for GLMs in general. Other papers contributed extensions directly from LMs to the general class of GLMs: score tests and related diagnostics (Pregibon, 1982), various forms of residuals (Gilchrist, 1981;Williams, 1984), deletion diagnostics (Williams, 1987), added variable and partial plots (Wang, 1985(Wang, , 1987O'Hara Hines and Carter, 1993).…”

Section: Introductionmentioning

confidence: 99%

A note on adjusted responses, fitted values and residuals in Generalized Linear Models

Lovison

2014

Statistical Modelling

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Adjusted responses, adjusted fitted values and adjusted residuals are known to play in Generalized Linear Models the role played in Linear Models by observations, fitted values and ordinary residuals. We think this parallelism, which was widely recognized and used in the early literature on Generalized Linear Models, has been somewhat overlooked in more recent presentations. We revise this parallelism, systematizing and proving some results that are either scattered or not satisfactorily spelled out in the literature. In particular, we formally derive the asymptotic dispersion matrix of the (scaled) adjusted residuals, by proving that in Generalized Linear Models the fitted values are asymptotically uncorrelated with the raw residuals and hence deriving the asymptotic dispersion matrix of these latter residuals. Also, we show that an orthogonal decomposition of the error vector between adjusted response and true linear predictor, parallel to the familiar decomposition in Linear Models, holds approximately. Finally, we provide some new perspective, both in Linear and Generalized Linear Models, on adjusted residuals for model comparison, and their relationships with test-statistics used to compare the fit of nested models.

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Improved Added Variable and Partial Residual Plots for the Detection of Influential Observations in Generalized Linear Models

Cited by 45 publications

References 29 publications

Selecting the number of classes under latent class regression: a factor analytic analogue

Selecting the number of classes under latent class regression: a factor analytic analogue

Plotting partial correlation and regression in ecological studies

A note on adjusted responses, fitted values and residuals in Generalized Linear Models

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