svycollinear: Condition indexes and variance decompositions in general...

In svydiags: Regression Model Diagnostics for Survey Data

Condition indexes and variance decompositions in general linear models (GLMs) fitted with complex survey data

Description

Compute condition indexes and variance decompositions for diagnosing collinearity in fixed effects, general linear regression models fitted with data collected from one- and two-stage complex survey designs.

Usage

svycollinear(mobj, X, w, sc=TRUE, rnd=3, fuzz=0.05)

Arguments

mobj	model object produced by svyglm. The following families of models are allowed: binomial and quasibinomial (logit and probit links), gaussian (identity link), poisson and quasipoisson (log link), Gamma (inverse link), and inverse.gaussian (1/mu^2 link). Other families or links allowed by svyglm will produce an error in svycollinear.
X	n \times p matrix of real-valued covariates used in fitting the regression; n = number of observations, p = number of covariates in model, excluding the intercept. A column of 1's for an intercept may be included if the model includes an intercept. X is most easily produced by the function model.matrix in the stats package, which will correctly code factors as 0-1. X should not contain columns for the strata and cluster identifiers (unless those variables are part of the model). No missing values are allowed.
w	n-vector of survey weights used in fitting the model. No missing values are allowed.
sc	TRUE if the columns of the weighted model matrix \tilde{\mathbf{X}} (defined in Details) should be scaled for computing condition indexes; FALSE if not. If TRUE, each column of \tilde{\mathbf{X}} is divided by its Euclidean norm, \sqrt{\tilde{\mathbf{x}}^T \tilde{\mathbf{x}}}.
rnd	Round the output to rnd decimal places.
fuzz	Replace any variance decomposition proportions that are less than fuzz by ‘.’ in the output.

Details

svycollinear computes condition indexes and variance decomposition proportions to use for diagnosing collinearity in a general linear model fitted from complex survey data as discussed in Liao (2010, ch. 5) and Liao and Valliant (2012). All measures are based on \widetilde{\mathbf{X}} = \mathbf{W}^{1/2}\hat{\mathbf{\Gamma}}\mathbf{X} where \mathbf{W} is the diagonal matrix of survey weights, \hat{\mathbf{\Gamma}} is a diagonal matrix of estimated parameters from the particular type of GLM, and X is the n \times p matrix of covariates. In a full-rank model with p covariates, there are p condition indexes, defined as the ratio of the maximum eigenvalue of \widetilde{\mathbf{X}} to each of the p eigenvalues. If sc=TRUE, before computing condition indexes, as recommended by Belsley (1991), the columns are normalized by their individual Euclidean norms, \sqrt{\tilde{\mathbf{x}}^T\tilde{\mathbf{x}}}, so that each column has unit length. The columns are not centered around their means because that can obscure near-dependencies between the intercept and other covariates (Belsley 1984).

Variance decompositions are for the variance of each estimated regression coefficient and are based on a singular value decomposition of the variance formula. For linear models, the decomposition is for the sandwich variance estimator, which has both a model-based and design-based interpretation. In the case of nonlinear GLMs (i.e., family is not gaussian), the variance is the approximate model variance. Proportions of the model variance, Var_M(\hat{\mathbf{\beta}}_k), associated with each column of \widetilde{\mathbf{X}} are displayed in an output matrix described below.

Value

p \times (p+1) data frame, \mathbf{\Pi}. The first column gives the condition indexes of \widetilde{\mathbf{X}}. Values of 10 or more are usually considered to potentially signal collinearity of two or more columns of \widetilde{\mathbf{X}}. The remaining columns give the proportions (within columns) of variance of each estimated regression coefficient associated with a singular value decomposition into p terms. Columns 2, \ldots, p+1 will each approximately sum to 1. When family=gaussian, some ‘proportions’ can be negative or greater than 1 due to the nature of the variance decomposition (see Liao and Valliant, 2012). For other families the proportions will be in [0,1]. If two proportions in a given row of \mathbf{\Pi} are relatively large and its associated condition index in that row in the first column of \mathbf{\Pi} is also large, then near dependencies between the covariates associated with those elements are influencing the regression coefficient estimates.

Author(s)

Richard Valliant

References

Belsley, D.A., Kuh, E. and Welsch, R.E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: Wiley-Interscience.

Belsley, D.A. (1984). Demeaning conditioning diagnostics through centering. The American Statistician, 38(2), 73-77.

Belsley, D.A. (1991). Conditioning Diagnostics, Collinearity, and Weak Data in Regression. New York: John Wiley & Sons, Inc.

Liao, D. (2010). Collinearity Diagnostics for Complex Survey Data. PhD thesis, University of Maryland. http://hdl.handle.net/1903/10881.

Liao, D, and Valliant, R. (2012). Condition indexes and variance decompositions for diagnosing collinearity in linear model analysis of survey data. Survey Methodology, 38, 189-202.

Lumley, T. (2010). Complex Surveys. New York: John Wiley & Sons.

Lumley, T. (2023). survey: analysis of complex survey samples. R package version 4.2.

See Also

svyvif

Examples

require(survey)
    # example from svyglm help page
data(api)
dstrat <- svydesign(id=~1,strata=~stype, weights=~pw, data=apistrat, fpc=~fpc)
    # linear model
m1 <- svyglm(api00 ~ ell + meals + mobility, design=dstrat)
X.model <- model.matrix(~ ell + meals + mobility, data = apistrat)
    # send model object from svyglm
svycollinear(mobj=m1, X=X.model, w=apistrat$pw, sc=TRUE, rnd=3, fuzz= 0.05)

    # logistic model
data(nhanes2007)
nhanes2007$obese <- nhanes2007$BMXBMI >= 30
nhanes.dsgn <- svydesign(ids = ~SDMVPSU,
                         strata = ~SDMVSTRA,
                         weights = ~WTDRD1, nest=TRUE, data=nhanes2007)
m2 <- svyglm(obese ~ RIDAGEYR + as.factor(RIDRETH1) + DR1TKCAL +
    DR1TTFAT + DR1TMFAT, design=nhanes.dsgn, family=quasibinomial())
X.model <- model.matrix(~ RIDAGEYR + as.factor(RIDRETH1) + DR1TKCAL + DR1TTFAT + DR1TMFAT,
        data = data.frame(nhanes2007))
svycollinear(mobj=m2, X=X.model, w=nhanes2007$WTDRD1, sc=TRUE, rnd=2, fuzz=0.05)

svydiags documentation built on April 3, 2025, 5:26 p.m.