EdSurvey Linear Models

Fits a linear model that uses weights and variance estimates appropriate for the data.

Usage

lm.sdf(formula, data, weightVar = NULL, relevels = list(),
              varMethod = c("jackknife", "Taylor"), jrrIMax = 1,
              dropOmittedLevels = TRUE, defaultConditions = TRUE, recode = NULL,
              returnVarEstInputs = FALSE, returnNumberOfPSU = FALSE,
              standardizeWithSamplingVar = FALSE, verbose=TRUE,
              omittedLevels = deprecated())

Arguments

formula: a formula for the linear model. See lm. If y is left blank, the default subject scale or subscale variable will be used. (You can find the default using showPlausibleValues.) If y is a variable for a subject scale or subscale (one of the names shown by showPlausibleValues), then that subject scale or subscale is used.
data: an edsurvey.data.frame, a light.edsurvey.data.frame, or an edsurvey.data.frame.list
weightVar: a character indicating the weight variable to use (see Details). The weightVar must be one of the weights for the edsurvey.data.frame. If NULL, it uses the default for the edsurvey.data.frame.
relevels: a list. Used to change the contrasts from the default treatment contrasts to the treatment contrasts with a chosen omitted group (the reference group). The name of each element should be the variable name, and the value should be the group to be omitted (the reference group).
varMethod: a character set to “jackknife” or “Taylor” that indicates the variance estimation method to be used. See Details.
jrrIMax: a numeric value; when using the jackknife variance estimation method, the default estimation option, jrrIMax=1, uses the sampling variance from the first plausible value as the component for sampling variance estimation. The Vjrr term (see Statistical Methods Used in EdSurvey) can be estimated with any number of plausible values, and values larger than the number of plausible values on the survey (including Inf) will result in all plausible values being used. Higher values of jrrIMax lead to longer computing times and more accurate variance estimates.
dropOmittedLevels: a logical value. When set to the default value of TRUE, drops those levels of all factor variables that are specified in an edsurvey.data.frame. Use print on an edsurvey.data.frame to see the omitted levels.
defaultConditions: a logical value. When set to the default value of TRUE, uses the default conditions stored in an edsurvey.data.frame to subset the data. Use print on an edsurvey.data.frame to see the default conditions.
recode: a list of lists to recode variables. Defaults to NULL. Can be set as recode=list(var1 = list(from= c("a", "b", "c"), to= "d")). See Examples.
returnVarEstInputs: a logical value set to TRUE to return the inputs to the jackknife and imputation variance estimates, which allow for the computation of covariances between estimates.
returnNumberOfPSU: a logical value set to TRUE to return the number of primary sampling units (PSUs)
standardizeWithSamplingVar: a logical value indicating if the standardized coefficients should have the variance of the regressors and outcome measured with sampling variance. Defaults to FALSE.
verbose: logical; indicates whether a detailed printout should display during execution
omittedLevels: this argument is deprecated. Use dropOmittedLevels

Value

An edsurvey.lm with the following elements:

call: the function call
formula: the formula used to fit the model
coef: the estimates of the coefficients
se: the standard error estimates of the coefficients
Vimp: the estimated variance from uncertainty in the scores (plausible value variables)
Vjrr: the estimated variance from sampling
M: the number of plausible values
varm: the variance estimates under the various plausible values
coefm: the values of the coefficients under the various plausible values
coefmat: the coefficient matrix (typically produced by the summary of a model)
r.squared: the coefficient of determination
weight: the name of the weight variable
npv: the number of plausible values
jrrIMax: the jrrIMax value used in computation
njk: the number of the jackknife replicates used; set to NA when Taylor series variance estimates are used
varMethod: one of Taylor series or the jackknife
residuals: residuals from the average regression coefficients
PV.residuals: residuals from the by plausible value coefficients
PV.fitted.values: fitted values from the by plausible value coefficients
B: imputation variance covariance matrix, before multiplication by (M+1)/M
U: sampling variance covariance matrix
rbar: average relative increase in variance; see van Buuren (2012, eq. 2.29)
nPSU: number of PSUs used in calculation
n0: number of rows on an edsurvey.data.frame before any conditions were applied
nUsed: number of observations with valid data and weights larger than zero
data: data used for the computation
Xstdev: standard deviations of regressors, used for computing standardized regression coefficients when standardizeWithSamplingVar is set to FALSE (the default)
varSummary: the result of running summary2 (unweighted) on each variable in the regression
varEstInputs: when returnVarEstInputs is TRUE, this element is returned. These are used for calculating covariances with varEstToCov.
standardizeWithSamplingVar: when standardizeWithSamplingVar is set to TRUE, this element is returned. Calculates the standard deviation of the standardized regression coefficients like any other variable.

Details

This function implements an estimator that correctly handles left-hand side variables that are either numeric or plausible values and allows for survey sampling weights and estimates variances using the jackknife replication method. The vignette titled Statistical Methods Used in EdSurvey describes estimation of the reported statistics.

Regardless of the variance estimation, the coefficients are estimated using the sample weights according to the sections “Estimation of Weighted Means When Plausible Values Are Not Present” or “Estimation of Weighted Means When Plausible Values Are Present,” depending on if there are assessment variables or variables with plausible values in them.

How the standard errors of the coefficients are estimated depends on the value of varMethod and the presence of plausible values (assessment variables), But once it is obtained, the t statistic is given by $$t=\frac{\hat{\beta}}{\sqrt{\mathrm{var}(\hat{\beta})}}$$ where $ \hat{\beta} $ is the estimated coefficient and $\mathrm{var}(\hat{\beta})$ is the variance of that estimate.

The coefficient of determination (R-squared value) is similarly estimated by finding the average R-squared using the average across the plausible values.

Standardized regression coefficients

Standardized regression coefficients can be returned in a call to summary, by setting the argument src to TRUE. See Examples.

By default, the standardized coefficients are calculated using standard deviations of the variables themselves, including averaging the standard deviation across any plausible values. When standardizeWithSamplingVar is set to TRUE, the variance of the standardized coefficient is calculated similar to a regression coefficient and therefore includes the sampling variance in the variance estimate of the outcome variable.

Variance estimation of coefficients

All variance estimation methods are shown in the vignette titled Statistical Methods Used in EdSurvey. When varMethod is set to the jackknife and the predicted value does not have plausible values, the variance of the coefficients is estimated according to the section “Estimation of Standard Errors of Weighted Means When Plausible Values Are Not Present, Using the Jackknife Method.”

When plausible values are present and varMethod is jackknife, the variance of the coefficients is estimated according to the section “Estimation of Standard Errors of Weighted Means When Plausible Values Are Present, Using the Jackknife Method.”

When plausible values are not present and varMethod is Taylor, the variance of the coefficients is estimated according to the section “Estimation of Standard Errors of Weighted Means When Plausible Values Are Not Present, Using the Taylor Series Method.”

When plausible values are present and varMethod is Taylor, the variance of the coefficients is estimated according to the section “Estimation of Standard Errors of Weighted Means When Plausible Values Are Present, Using the Taylor Series Method.”

Testing

Of the common hypothesis tests for joint parameter testing, only the Wald test is widely used with plausible values and sample weights. As such, it replaces, if imperfectly, the Akaike Information Criteria (AIC), the likelihood ratio test, chi-squared, and analysis of variance (ANOVA, including F-tests). See waldTest or the vignette titled Methods and Overview of Using EdSurvey for Running Wald Tests.

References

Binder, D. A. (1983). On the variances of asymptotically normal estimators from complex surveys. International Statistical Review, 51(3), 279–292.

Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys. New York, NY: Wiley.

van Buuren, S. (2012). Flexible imputation of missing data. New York, NY: CRC Press.

Weisberg, S. (1985). Applied linear regression (2nd ed.). New York, NY: Wiley.

Author

Paul Bailey

Examples

if (FALSE) { # \dontrun{
# read in the example data (generated, not real student data)
sdf <- readNAEP(path=system.file("extdata/data", "M36NT2PM.dat", package = "NAEPprimer"))

# by default uses jackknife variance method using replicate weights
lm1 <- lm.sdf(formula=composite ~ dsex + b017451, data=sdf)
lm1

# the summary function displays detailed results
summary(lm1)

# to show standardized regression coefficients
summary(lm1, src=TRUE)

# to specify a variance method, use varMethod
lm2 <- lm.sdf(formula=composite ~ dsex + b017451, data=sdf, varMethod="Taylor")
lm2
summary(lm2)

# use relevel to set a new omitted category
lm3 <- lm.sdf(formula=composite ~ dsex + b017451, data=sdf, relevels=list(dsex="Female"))
summary(lm3)
# test of a simple joint hypothesis
waldTest(lm3, "b017451")

# use recode to change values for specified variables
lm4 <- lm.sdf(formula=composite ~ dsex + b017451, data=sdf,
              recode=list(b017451=list(from=c("Never or hardly ever",
                                              "Once every few weeks",
                                              "About once a week"),
                                       to=c("Infrequently")),
                          b017451=list(from=c("2 or 3 times a week","Every day"),
                                       to=c("Frequently"))))
# Note: "Infrequently" is the dropped level for the recoded b017451
summary(lm4)

# use plausible values as predictors in a linear regression model
lm5 <- lm.sdf(formula=algebra ~ dsex + geometry, data=sdf)
lm5
summary(lm5)
} # }