Type: Package
Title: Regression Model Diagnostics for Survey Data
Version: 0.7
Date: 2024-11-05
Author: Richard Valliant [aut, cre]
Maintainer: Richard Valliant <valliant@umich.edu>
Description: Diagnostics for fixed effects linear and general linear regression models fitted with survey data. Extensions of standard diagnostics to complex survey data are included: standardized residuals, leverages, Cook's D, dfbetas, dffits, condition indexes, and variance inflation factors as found in Li and Valliant (Surv. Meth., 2009, 35(1), pp. 15-24; Jnl. of Off. Stat., 2011, 27(1), pp. 99-119; Jnl. of Off. Stat., 2015, 31(1), pp. 61-75); Liao and Valliant (Surv. Meth., 2012, 38(1), pp. 53-62; Surv. Meth., 2012, 38(2), pp. 189-202). Variance inflation factors and condition indexes are also computed for some general linear models as described in Liao (U. Maryland thesis, 2010).
Suggests: doBy, foreign, NHANES, sampling
Depends: MASS, Matrix, survey
License: GPL-3
LazyLoad: yes
LazyData: true
NeedsCompilation: no
Packaged: 2024-11-08 17:49:14 UTC; rv
Repository: CRAN
Date/Publication: 2024-11-08 18:30:02 UTC

Compute covariance matrix of residuals for general linear models fitted with complex survey data

Description

Compute a covariance matrix using residuals from a fixed effects, general linear regression model fitted with data collected from one- and two-stage complex survey designs.

Usage

Vmat(mobj, stvar = NULL, clvar = NULL)

Arguments

mobj

model object produced by svyglm

stvar

field in mobj that contains the stratum variable in the complex sample design; use stvar = NULL if there are no strata

clvar

field in mobj that contains the cluster variable in the complex sample design; use clvar = NULL if there are no clusters

Details

Vmat computes a covariance matrix among the residuals returned from svyglm in the survey package. Vmat is called by svyvif when computing variance inflation factors. The matrix that is computed by Vmat is appropriate under these model assumptions: (1) in single-stage, unclustered sampling, units are assumed to be uncorrelated but can have different model variances, (2) in single-stage, stratified sampling, units are assumed to be uncorrelated within strata and between strata but can have different model variances; (3) in unstratified, clustered samples, units in different clusters are assumed to be uncorrelated but units within clusters are correlated; (3) in stratified, clustered samples, units in different strata or clusters are assumed to be uncorrelated but units within clusters are correlated.

Value

n \times n matrix where n is the number of cases used in the linear regression model

Author(s)

Richard Valliant

References

Liao, D, and Valliant, R. (2012). Variance inflation factors in the analysis of complex survey data. Survey Methodology, 38, 53-62.

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(Matrix)
require(survey)
data(nhanes2007)
black <- nhanes2007$RIDRETH1 == 4
X <- nhanes2007
X <-  cbind(X, black)
X1 <- X[order(X$SDMVSTRA, X$SDMVPSU),]

    # unstratified, unclustered design
nhanes.dsgn <- svydesign(ids = 1:nrow(X1),
                         strata = NULL,
                         weights = ~WTDRD1, data=X1)
m1 <- svyglm(BMXWT ~ RIDAGEYR + as.factor(black) + DR1TKCAL, design=nhanes.dsgn)
summary(m1)

V <- Vmat(mobj = m1,
          stvar = NULL,
          clvar = NULL)

    # stratified, clustered design
nhanes.dsgn <- svydesign(ids = ~SDMVPSU,
                         strata = ~SDMVSTRA,
                         weights = ~WTDRD1, nest=TRUE, data=X1)
m1 <- svyglm(BMXWT ~ RIDAGEYR + as.factor(black) + DR1TKCAL, design=nhanes.dsgn)
summary(m1)
V <- Vmat(mobj = m1,
          stvar = "SDMVSTRA",
          clvar = "SDMVPSU")

National Health and Nutrition Examination Survey data, 2007-2008

Description

Demographic and dietary intake variables from a U.S. national household survey

Usage

data(nhanes2007)

Format

A data frame with 4,329 person-level observations on the following 26 variables measuring 24-hour dietary recall. See https://wwwn.cdc.gov/nchs/nhanes/2013-2014/DR2IFF_H.htm for more details about the variables.

SEQN

Identification variable

SDMVSTRA

Stratum

SDMVPSU

Primary sampling unit, numbered within each stratum (1,2)

WTDRD1

Dietary day 1 sample weight

GENDER

Gender (0 = female; 1 = male)

RIDAGEYR

Age in years at the time of the screening interview; reported for survey participants between the ages of 1 and 79 years of age. All responses of participants aged 80 years and older are coded as 80.

RIDRETH1

Race/Hispanic origin (1 = Mexican American; 2 = Other Hispanic; 3 = Non-Hispanic White; 4 = Non-Hispanic Black; 5 = Other Race including multiracial)

BMXWT

Body weight (kg)

BMXBMI

Body mass Index ((weight in kg) / (height in meters)**2)

DIET

On any diet (0 = No; 1 = Yes)

CALDIET

On a low-calorie diet (0 = No; 1 = Yes)

FATDIET

On a low-fat diet (0 = No; 1 = Yes)

CARBDIET

On a low-carbohydrate diet (0 = No; 1 = Yes)

DR1DRSTZ

Dietary recall status that indicates quality and completeness of survey participant's response to dietary recall section. (1 = Reliable and met the minimum criteria; 2 = Not reliable or not met the minimum criteria; 4 = Reported consuming breast-milk (infants and children only))

DR1TKCAL

Energy (kcal)

DR1TPROT

Protein (gm)

DR1TCARB

Carbohydrate (gm)

DR1TSUGR

Total sugars (gm)

DR1TFIBE

Dietary fiber (gm)

DR1TTFAT

Total fat (gm)

DR1TSFAT

Total saturated fatty acids (gm)

DR1TMFAT

Total monounsaturated fatty acids (gm)

DR1TPFAT

Total polyunsaturated fatty acids (gm)

DR1TCAFF

Caffeine (mg)

DR1TALCO

Alcohol (gm)

DR1_320Z

Total plain water drank yesterday (gm)

Details

The National Health and Nutrition Examination Survey (NHANES) is a program of studies designed to assess the health and nutritional status of adults and children in the United States. The survey is unique in that it combines interviews and physical examinations. The nhis2007 data set contains observations for 4,329 persons collected in 2007-2008.

Source

National Health and Nutrition Examination Survey of 2007-2008 conducted by the U.S. National Center for Health Statistics. https://www.cdc.gov/nchs/nhanes.htm

Examples

data(nhanes2007)
str(nhanes2007)
summary(nhanes2007)

Modified Cook's D for models fitted with complex survey data

Description

Compute a modified Cook's D for fixed effects, linear regression models fitted with data collected from one- and two-stage complex survey designs.

Usage

svyCooksD(mobj, stvar=NULL, clvar=NULL, doplot=FALSE)

Arguments

mobj

model object produced by svyglm in the survey package

stvar

name of the stratification variable in the svydesign object used to fit the model

clvar

name of the cluster variable in the svydesign object used to fit the model

doplot

if TRUE, plot the modified Cook's D values vs. their sequence number in data set. Reference lines are drawn at 2 and 3

Details

svyCooksD computes the modified Cook's D (m-cook; see Atkinson (1982) and Li & Valliant (2011, 2015)) which measures the effect on the vector of parameter estimates of deleting single observations when fitting a fixed effects regression model to complex survey data. The function svystdres is called for some of the calculations. Values of m-cook are considered large if they are greater than 2 or 3. The R package MASS must also be loaded before calling svyCooksD. The output is a vector of the m-cook values and a scatterplot of them versus the sequence number of the sample element used in fitting the model. By default, svyglm uses only complete cases (i.e., ones for which the dependent variable and all independent variables are non-missing) to fit the model. The rows of the data frame used in fitting the model can be retrieved from the svyglm object via as.numeric(names(mobj$y)). The data for those rows is in mobj$data.

Value

Numeric vector whose names are the rows of the data frame in the svydesign object that were used in fitting the model

Author(s)

Richard Valliant

References

Atkinson, A.C. (1982). Regression diagnostics, transformations and constructed variables (with discussion). Journal of the Royal Statistical Society, Series B, Methodological, 44, 1-36.

Cook, R.D. (1977). Detection of Influential Observation in Linear Regression. Technometrics, 19, 15-18.

Cook, R.D. and Weisberg, S. (1982). Residuals and Influence in Regression. London:Chapman & Hall Ltd.

Li, J., and Valliant, R. (2011). Linear regression diagnostics for unclustered survey data. Journal of Official Statistics, 27, 99-119.

Li, J., and Valliant, R. (2015). Linear regression diagnostics in cluster samples. Journal of Official Statistics, 31, 61-75.

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

svydfbetas, svydffits, svystdres

Examples

require(MASS)   # to get ginv
require(survey)
data(api)
    # unstratified design single stage design
d0 <- svydesign(id=~1,strata=NULL, weights=~pw, data=apistrat)
m0 <- svyglm(api00 ~ ell + meals + mobility, design=d0)
mcook <- svyCooksD(m0, doplot=TRUE)

    # stratified clustered design
require(NHANES)
data(NHANESraw)
dnhanes <- svydesign(id=~SDMVPSU, strata=~SDMVSTRA, weights=~WTINT2YR, nest=TRUE, data=NHANESraw)
m2 <- svyglm(BPDiaAve ~ as.factor(Race1) + BMI + AlcoholYear, design = dnhanes)
mcook <- svyCooksD(mobj=m2, stvar="SDMVSTRA", clvar="SDMVPSU", doplot=TRUE)

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)

dfbetas for models fitted with complex survey data

Description

Compute the dfbetas measure of the effect of extreme observations on parameter estimates for fixed effects, linear regression models fitted with data collected from one- and two-stage complex survey designs.

Usage

svydfbetas(mobj, stvar=NULL, clvar=NULL, z=3)

Arguments

mobj

model object produced by svyglm in the survey package

stvar

name of the stratification variable in the svydesign object used to fit the model

clvar

name of the cluster variable in the svydesign object used to fit the model

z

numerator of cutoff for measuring whether an observation has an extreme effect on its own predicted value; default is 3 but can be adjusted to control how many observations are flagged for inspection

Details

svydfbetas computes the values of dfbetas for each observation and parameter estimate, i.e., the amount that a parameter estimate changes when the unit is deleted from the sample. The model object must be created by svyglm in the R survey package. The output is a vector of the dfbeta and standardized dfbetas values. By default, svyglm uses only complete cases (i.e., ones for which the dependent variable and all independent variables are non-missing) to fit the model. The rows of the data frame used in fitting the model can be retrieved from the svyglm object via as.numeric(names(mobj$y)). The data for those rows is in mobj$data.

Value

List object with values:

Dfbeta

Numeric vector of unstandardized dfbeta values whose names are the rows of the data frame in the svydesign object that were used in fitting the model

Dfbetas

Numeric vector of standardized dfbetas values whose names are the rows of the data frame in the svydesign object that were used in fitting the model

cutoff

Value used for gauging whether a value of dffits is large. For a single-stage sample, cutoff=z/\sqrt{n}; for a 2-stage sample, cutoff=z/\sqrt{n[1+\rho (\bar{m}-1)]}

Author(s)

Richard Valliant

References

Li, J., and Valliant, R. (2011). Linear regression diagnostics for unclustered survey data. Journal of Official Statistics, 27, 99-119.

Li, J., and Valliant, R. (2015). Linear regression diagnostics in cluster samples. Journal of Official Statistics, 31, 61-75.

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

svydffits, svyCooksD

Examples

require(survey)
data(api)
    # unstratified design single stage design
d0 <- svydesign(id=~1,strata=NULL, weights=~pw, data=apistrat)
m0 <- svyglm(api00 ~ ell + meals + mobility, design=d0)
svydfbetas(mobj=m0)

    # stratified cluster
require(NHANES)
data(NHANESraw)
dnhanes <- svydesign(id=~SDMVPSU, strata=~SDMVSTRA, weights=~WTINT2YR, nest=TRUE, data=NHANESraw)
m2 <- svyglm(BPDiaAve ~ as.factor(Race1) + BMI + AlcoholYear, design = dnhanes)
yy <- svydfbetas(mobj=m2, stvar= "SDMVSTRA", clvar="SDMVPSU")
apply(abs(yy$Dfbetas) > yy$cutoff,1, sum)

dffits for models fitted with complex survey data

Description

Compute the dffits measure of the effect of extreme observations on predicted values for fixed effects, linear regression models fitted with data collected from one- and two-stage complex survey designs.

Usage

svydffits(mobj, stvar=NULL, clvar=NULL, z=3)

Arguments

mobj

model object produced by svyglm in the survey package

stvar

name of the stratification variable in the svydesign object used to fit the model

clvar

name of the cluster variable in the svydesign object used to fit the model

z

numerator of cutoff for measuring whether an observation has an extreme effect on its own predicted value; default is 3 but can be adjusted to control how many observations are flagged for inspection

Details

svydffits computes the value of dffits for each observation, i.e., the amount that a unit's predicted value changes when the unit is deleted from the sample. The model object must be created by svyglm in the R survey package. The output is a vector of the dffit and standardized dffits values. By default, svyglm uses only complete cases (i.e., ones for which the dependent variable and all independent variables are non-missing) to fit the model. The rows of the data frame used in fitting the model can be retrieved from the svyglm object via as.numeric(names(mobj$y)). The data for those rows is in mobj$data.

Value

List object with values:

Dffit

Numeric vector of unstandardized dffit values whose names are the rows of the data frame in the svydesign object that were used in fitting the model

Dffits

Numeric vector of standardized dffits values whose names are the rows of the data frame in the svydesign object that were used in fitting the model

cutoff

Value used for gauging whether a value of dffits is large. For a single-stage sample, cutoff=z/\sqrt{n}; for a 2-stage sample, cutoff=z\sqrt{p/n\bar{m}[1+\rho (\bar{m}-1)]}

Author(s)

Richard Valliant

References

Li, J., and Valliant, R. (2011). Linear regression diagnostics for unclustered survey data. Journal of Official Statistics, 27, 99-119.

Li, J., and Valliant, R. (2015). Linear regression diagnostics in cluster samples. Journal of Official Statistics, 31, 61-75.

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

svydfbetas, svyCooksD

Examples

require(survey)
data(api)
    # unstratified design single stage design
d0 <- svydesign(id=~1,strata=NULL, weights=~pw, data=apistrat)
m0 <- svyglm(api00 ~ ell + meals + mobility, design=d0)
yy <- svydffits(mobj=m0)
yy$cutoff
sum(abs(yy$Dffits) > yy$cutoff)

require(NHANES)
data(NHANESraw)
dnhanes <- svydesign(id=~SDMVPSU, strata=~SDMVSTRA, weights=~WTINT2YR, nest=TRUE, data=NHANESraw)
m2 <- svyglm(BPDiaAve ~ as.factor(Race1) + BMI + AlcoholYear, design = dnhanes)
yy <- svydffits(mobj=m2, stvar= "SDMVSTRA", clvar="SDMVPSU", z=4)
sum(abs(yy$Dffits) > yy$cutoff)

Leverages for models fitted with complex survey data

Description

Compute leverages for fixed effects, linear regression models fitted from complex survey data.

Usage

svyhat(mobj, doplot=FALSE)

Arguments

mobj

model object produced by svyglm in the survey package

doplot

if TRUE, plot the standardized residuals vs. their sequence number in data set. A reference line is drawn at 3 times the mean leverage

Details

svyhat computes the leverages from a model fitted with complex survey data. The model object mobj must be created by svyglm in the R survey package. The output is a vector of the leverages and a scatterplot of them versus the sequence number of the sample element used in fitting the model. By default, svyglm uses only complete cases (i.e., ones for which the dependent variable and all independent variables are non-missing) to fit the model. The rows of the data frame used in fitting the model can be retrieved from the svyglm object via as.numeric(names(mobj$y)). The data for those rows is in mobj$data.

Value

Numeric vector whose names are the rows of the data frame in the svydesign object that were used in fitting the model.

Author(s)

Richard Valliant

References

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

Li, J., and Valliant, R. (2009). Survey weighted hat matrix and leverages. Survey Methodology, 35, 15-24.

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

svystdres

Examples

require(survey)
data(api)
dstrat <- svydesign(id=~1,strata=~stype, weights=~pw, data=apistrat)
m1 <- svyglm(api00 ~ ell + meals + mobility, design=dstrat)
h <- svyhat(mobj = m1, doplot=TRUE)
100*sum(h > 3*mean(h))/length(h)    # percentage of leverages > 3*mean

require(NHANES)
data(NHANESraw)
dnhanes <- svydesign(id=~SDMVPSU, strata=~SDMVSTRA, weights=~WTINT2YR, nest=TRUE, data=NHANESraw)
m1 <- svyglm(BPDiaAve ~ as.factor(Race1) + BMI + AlcoholYear, design = dnhanes)
h <- svyhat(mobj = m1, doplot=TRUE)

Standardized residuals for models fitted with complex survey data

Description

Compute standardized residuals for fixed effects, linear regression models fitted with data collected from one- and two-stage complex survey designs.

Usage

svystdres(mobj, stvar=NULL, clvar=NULL, doplot=FALSE)

Arguments

mobj

model object produced by svyglm in the survey package

stvar

name of the stratification variable in the svydesign object used to fit the model

clvar

name of the cluster variable in the svydesign object used to fit the model

doplot

if TRUE, plot the standardized residuals vs. their sequence number in data set. Reference lines are drawn at +/-3

Details

svystdres computes the standardized residuals, i.e., the residuals divided by an estimate of the model standard deviation of the residuals. Residuals are used from a model object created by svyglm in the R survey package. The output is a vector of the standardized residuals and a scatterplot of them versus the sequence number of the sample element used in fitting the model. By default, svyglm uses only complete cases (i.e., ones for which the dependent variable and all independent variables are non-missing) to fit the model. The rows of the data frame used in fitting the model can be retrieved from the svyglm object via as.numeric(names(mobj$y)). The data for those rows is in mobj$data.

Value

List object with values:

stdresids

Numeric vector whose names are the rows of the data frame in the svydesign object that were used in fitting the model

n

number of sample clusters

mbar

average number of non-missing, sample elements per cluster

rtsighat

estimate of the square root of the model variance of the residuals, \sigma

rhohat

estimate of the intracluster correlation of the residuals, \rho

Author(s)

Richard Valliant

References

Li, J., and Valliant, R. (2011). Linear regression diagnostics for unclustered survey data. Journal of Official Statistics, 27, 99-119.

Li, J., and Valliant, R. (2015). Linear regression diagnostics in cluster samples. Journal of Official Statistics, 31, 61-75.

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

svyhat, svyCooksD

Examples

require(survey)
data(api)
    # unstratified design single stage design
d0 <- svydesign(id=~1,strata=NULL, weights=~pw, data=apistrat)
m0 <- svyglm(api00 ~ ell + meals + mobility, design=d0)
svystdres(mobj=m0, stvar=NULL, clvar=NULL)

    # stratified cluster design
require(NHANES)
data(NHANESraw)
dnhanes <- svydesign(id=~SDMVPSU, strata=~SDMVSTRA, weights=~WTINT2YR, nest=TRUE, data=NHANESraw)
m1 <- svyglm(BPDiaAve ~ as.factor(Race1) + BMI + AlcoholYear, design = dnhanes)
svystdres(mobj=m1, stvar= "SDMVSTRA", clvar="SDMVPSU")

Variance inflation factors (VIF) for general linear models fitted with complex survey data

Description

Compute a VIF for fixed effects, general linear regression models fitted with data collected from one- and two-stage complex survey designs.

Usage

svyvif(mobj, X, w, stvar=NULL, clvar=NULL)

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 svyvif.

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 should not be included. 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.

stvar

field in mobj that contains the stratum variable in the complex sample design; use stvar = NULL if there are no strata

clvar

field in mobj that contains the cluster variable in the complex sample design; use clvar = NULL if there are no clusters

Details

svyvif computes variance inflation factors (VIFs) appropriate for linear models and some general linear models (GLMs) fitted from complex survey data (see Liao 2010 and Liao & Valliant 2012). A VIF measures the inflation of a slope estimate caused by nonorthogonality of the predictors over and above what the variance would be with orthogonality (Theil 1971; Belsley, Kuh, and Welsch 1980). A VIF may also be thought of as the amount that the variance of an estimated coefficient for a predictor x is inflated in a model that includes all x's compared to a model that includes only the single x. Another alternative is to use as a comparison a model that includes an intercept and the single x. Both of these VIFs are in the output.

The standard, non-survey data VIF equals 1/(1 - R^2_k) where R_k is the multiple correlation of the k^{th} column of X regressed on the remaining columns. The complex sample value of the VIF for a linear model consists of the standard VIF multiplied by two adjustments denoted in the output as zeta and either varrho.m or varrho. The VIF for a GLM is similar (Liao 2010, chap. 5; Liao & Valliant 2024). There is no widely agreed-upon cutoff value for identifying high values of a VIF, although 10 is a common suggestion.

Value

A list with two components:

Intercept adjusted

p \times 6 data frame with columns:

svy.vif.m:

complex sample VIF where the reference model includes an intercept and a single x

reg.vif.m:

standard VIF, 1/(1 - R^2_{m(k)}), that omits the factors, zeta and varrho.m; R^2_{m(k)} is an R-square, corrected for the mean, from a weighted least squares regression of the k^{th} x on the other x's in the regression

zeta:

1st multiplicative adjustment to reg.vif.m

varrho.m:

2nd multiplicative adjustment to reg.vif.m

zeta.x.varrho.m:

product of the two adjustments to reg.vif.m

Rsq.m:

R-square, corrected for the mean, in the regression of the k^{th} x on the other x's, including an intercept

No intercept

p \times 6 data frame with columns:

svy.vif:

complex sample VIF where the reference model includes a single x and excludes an intercept; this VIF is analogous to the one included in standard packages that provide VIFs for linear regressions

reg.vif:

standard VIF, 1/(1 - R^2_k), that omits the factors, zeta and varrho; R^2_k is an R-square, not corrected for the mean, from a weighted least squares regression of the k^{th} x on the other x's in the regression

zeta:

1st multiplicative adjustment to reg.vif

varrho:

2nd multiplicative adjustment to reg.vif

zeta.x.varrho:

product of the two adjustments to reg.vif

Rsq:

R-square, not corrected for the mean, in the regression of the k^{th} x on the other x's, including an intercept

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.

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). Variance inflation factors in the analysis of complex survey data. Survey Methodology, 38, 53-62.

Liao, D, and Valliant, R. (2024). Collinearity Diagnostics in Generalized Linear Models Fitted with Survey Data. submitted.

Theil, H. (1971). Principles of Econometrics. New York: John Wiley & Sons, Inc.

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

Lumley, T. (2023). survey: analysis of complex survey samples. R package version 4.4.

See Also

Vmat

Examples

require(survey)
data(nhanes2007)
X1 <- nhanes2007[order(nhanes2007$SDMVSTRA, nhanes2007$SDMVPSU),]
    # eliminate cases with missing values
delete <- which(complete.cases(X1)==FALSE)
X2 <- X1[-delete,]
X2$obese <- X2$BMXBMI >= 30
nhanes.dsgn <- svydesign(ids = ~SDMVPSU,
                         strata = ~SDMVSTRA,
                         weights = ~WTDRD1, nest=TRUE, data=X2)
    # linear model
m1 <- svyglm(BMXWT ~ RIDAGEYR + as.factor(RIDRETH1) + DR1TKCAL
            + DR1TTFAT + DR1TMFAT, design=nhanes.dsgn)
summary(m1)
    # construct X matrix using model.matrix from stats package
X3 <- model.matrix(~ RIDAGEYR + as.factor(RIDRETH1) + DR1TKCAL + DR1TTFAT + DR1TMFAT,
        data = data.frame(X2))
    # remove col of 1's for intercept with X3[,-1]
svyvif(mobj=m1, X=X3[,-1], w = X2$WTDRD1, stvar="SDMVSTRA", clvar="SDMVPSU")

    # Logistic model
m2 <- svyglm(obese ~ RIDAGEYR + as.factor(RIDRETH1) + DR1TKCAL
             + DR1TTFAT + DR1TMFAT, design=nhanes.dsgn, family="quasibinomial")
summary(m2)
svyvif(mobj=m2, X=X3[,-1], w = X2$WTDRD1, stvar = "SDMVSTRA", clvar = "SDMVPSU")