na.auxiliary: Auxiliary Variables Analysis

In misty: Miscellaneous Functions 'T. Yanagida'

Auxiliary Variables Analysis

Description

This function computes (1) a matrix with Pearson product-moment correlation for continuous variables, multiple correlation coefficient for categorical and continuous variables, and Phi coefficient and Cramer's V for categorical variables to identify variables related to the incomplete variable (i.e., correlates of incomplete variables), (2) a matrix with Cohen's d, Phi coefficient and Cramer's V for comparing cases with and without missing values, and (3) semi-partial correlations of an outcome variable conditional on the predictor variables of a substantive model with a set of candidate auxiliary variables to identify correlates of an incomplete outcome variable as suggested by Raykov and West (2016).

Usage

na.auxiliary(data, ..., model = NULL, categ = NULL, estimator = c("ML", "MLR"),
             missing = c("fiml", "two.stage", "robust.two.stage", "doubly.robust"),
             adjust = TRUE, weighted = FALSE, correct = FALSE,
             tri = c("both", "lower", "upper"), digits = 2, p.digits = 3,
             as.na = NULL, write = NULL, append = TRUE,
             check = TRUE, output = TRUE)

Arguments

data	a data frame with incomplete data, where missing values are coded as NA.
...	an expression indicating the variable names in data, e.g., na.auxiliary(dat, x1, x2, x3). Categorical variables specified in the argument categ can be, but do not need to be selected using the ... argument. Note that the operators +, -, ~, :, ::, and ! can also be used to select variables, see 'Details' in the df.subset function.
model	a character string specifying the substantive model predicting a continuous outcome variable using a set of predictor variables to estimate semi-partial correlations between the outcome variable and a set of candidate auxiliary variables. The default setting is model = NULL, i.e., the function computes Pearson product-moment correlation matrix and Cohen's d matrix.
categ	a character vector specifying the variables that are treated as categorical (see 'Details'). Note that variables that are factors or character vectors will be automatically added to the argument categ. Categorical variables will be excluded from the analysis when specifying the model argument to compute semi-partial correlations.
estimator	a character string indicating the estimator to be used when estimating semi-partial correlation coefficients, i.e., "ML" for maximum likelihood parameter estimates with conventional standard errors or "MLR" (default) maximum likelihood parameter estimates with Huber-White robust standard errors.
missing	a character string indicating how to deal with missing data when estimating semi-partial correlation coefficients, i.e., "fiml" for full information maximum likelihood method, two.stage for two-stage maximum likelihood method, robust.two.stage for robust two-stage maximum likelihood method, and doubly-robust for doubly-robust method (see 'Details' in the item.cfa function). The default setting is missing = "fiml".
adjust	logical: if TRUE (default), phi coefficient is adjusted by relating the coefficient to the possible maximum and Cramer's V is corrected for small-sample bias.
weighted	logical: if TRUE (default), the weighted pooled standard deviation is used when computing Cohen's d.
correct	logical: if TRUE, correction factor for Cohen's d to remove positive bias in small samples is used.
tri	a character string indicating which triangular of the correlation matrix to show on the console, i.e., both for upper and lower triangular, lower (default) for the lower triangular, and upper for the upper triangular.
digits	integer value indicating the number of decimal places digits to be used for displaying correlation coefficients and Cohen's d estimates.
p.digits	an integer value indicating the number of decimal places to be used for displaying the p-value.
as.na	a numeric vector indicating user-defined missing values, i.e. these values are converted to NA before conducting the analysis.
write	a character string naming a file for writing the output into either a text file with file extension ".txt" (e.g., "Output.txt") or Excel file with file extension ".xlsx" (e.g., "Output.xlsx"). If the file name does not contain any file extension, an Excel file will be written.
append	logical: if TRUE (default), output will be appended to an existing text file with extension .txt specified in write, if FALSE existing text file will be overwritten.
check	logical: if TRUE (default), argument specification is checked.
output	logical: if TRUE (default), output is shown on the console.

Details

The function computes matrices with statistical measures depending on the level of measurement of the variables involved in the analysis:

Variables Related to the Incomplete Variable

• Continuous variables: Product-moment correlation coefficient is computed for continuous variables.

• Continuous and categorical variable: Multiple correlation coefficient (R) is computed based on a linear model with a dummy-coded categorical variable as predictor, where the multiple correlation coefficient is the square root of the coefficient of determination of this model. Note that the multiple R for a binary predictor variable is equivalent to the point-biserial correlation coefficient between the binary variable and the continuous outcome.

• Categorical variables: Phi coefficient is computed for two dichotomous variables, while Cramer's V is computed when one of the categorical variables is polyotomous

Variables Related to the Probability of Missigness

• Continuous variable: Cohen's d is computed to investigate mean differences in the continuous variable depending on cases with and without missing values.

• Categorical variable: Phi coefficient is computed to investigate the association between the grouping variable (0 = observed, 1 = missing) and a dichotomous variable, while Cramer's V is computed when the categorical variable is polytomous.

Substantive model predicting a continuous outcome variable

Categorical variables are removed before computing semi-partial correlations based on the approach suggested by Raykov and West (2016).

Note that factors and characters are treated as categorical variables regardless of the specification of the argument categ, while numeric vectors in the data frame are treated as continuous variables if they are not specified in the argument categ.

Value

Returns an object of class misty.object, which is a list with following entries:

call	function call
type	type of analysis
data	data frame used for the current analysis
model	lavaan model syntax for estimating the semi-partial correlations
model.fit	fitted lavaan model for estimating the semi-partial correlations
args	pecification of function arguments
result	list with result tables

Author(s)

Takuya Yanagida [e-mail]

References

Enders, C. K. (2022). Applied missing data analysis (2nd ed.). The Guilford Press.

Graham, J. W. (2009). Missing data analysis: Making it work in the real world. Annual Review of Psychology, 60, 549-576. https://doi.org/10.1146/annurev.psych.58.110405.085530

Raykov, T., & West, B. T. (2016). On enhancing plausibility of the missing at random assumption in incomplete data analyses via evaluation of response-auxiliary variable correlations. Structural Equation Modeling, 23(1), 45–53. https://doi.org/10.1080/10705511.2014.937848

van Buuren, S. (2018). Flexible imputation of missing data (2nd ed.). Chapman & Hall.

See Also

as.na, na.as, na.coverage, na.descript, na.indicator, na.pattern, na.prop, na.test

Examples

# Example 1a: Auxiliary variables
na.auxiliary(airquality)

# Example 1b: Auxiliary variables, "Month" as categorical variable
na.auxiliary(airquality, categ = "Month")

# Example 2: Semi-partial correlation coefficients
na.auxiliary(airquality, model = "Ozone ~ Solar.R + Wind")

## Not run: 
# Example 3a: Write Results into a text file
na.auxiliary(airquality, write = "NA_Auxiliary.txt")

# Example 3a: Write Results into an Excel file
na.auxiliary(airquality, write = "NA_Auxiliary.xlsx")

## End(Not run)

misty documentation built on Nov. 5, 2025, 7:07 p.m.