These are some helper functions I’ve written in R and SPSS to go along with EDPY 678 Statistics in Applied Fields III, EDPY 680 Advanced Educational Measurement, and EDPY 667 Multilevel Modeling.

See CRAN for mlmhelpr: A collection of miscellaneous helper functions for running multilevel/mixed models in the lme4 package in R. See Github for utkesm: A collection of helper functions for the University of Tennessee, Knoxville (UTK) Evaluation, Statistics, and Methodology (ESM) program.

R

Quick Frequency and Descriptive Statistics

The majority of my students come to R after using SPSS for most of their careers. One issue they seem to grapple with is running frequency statistics in R. While there are many packages that provide descriptive statistics (e.g., psych::describe, skimr::skim), I wanted (1) a lightweight function that just prints frequency tables for all variables in a data frame, including NAs, regardless of type (e.g., factor, numeric): freq and (2) a function that prints a frequency table, including NAs, valid cases, and proportions, for factor variables and descriptive statistics (min, 1st quartile, median, 3rd quartile, max, mean, standard deviation, and number of missing cases) for numeric variables: stats. There is also an auxiliary function, freq2 that prints a frequency table along with number missing and proportions for all variables in a data frame regardless of type.

Each function requires only one argument, the name of the data frame object stored in R. Note: stats only works if every variable in the data frame is either a factor or numeric variable. Character variables will throw an error cause the function not to work.

freq(myData)
stats(myData)
freq2(myData)

You can download the file here or source it directly from the website: source("https://lrocconi.github.io/files/software/freqstats.R")

Structure Matrix

This function computes the Structure Matrix for a psych::fa object. When using an oblique rotation (e.g., oblimin, promax) in exploratory factor analysis, the factor loadings and correlations between the variables and factors are distinct. The Pattern Matrix contains the loadings while the Structure Matrix contains the correlation between variables and factors. The psych::fa function only prints the Pattern Matrix. To get the Structure Matrix, we need to multiple the pattern matrix by the correlations between the factors (e.g., fit$loadings %*% fit$Phi). This function performs this operation as well as suppresses correlations below a user-defined threshold and sorts the variables by their correlation with factor for easy reading.

The arguments in the function include:

• x Output from psych::fa function
• cut Correlations less than cut will not be printed; cut defaults to .32

Example structureMatrix(fa_1, .4)

You can download the file here or source it directly from the website: source("https://lrocconi.github.io/files/software/structureMatrix.R")

Item Complexity

This function compute Hoffman’s item complexity index. This is mainly for teaching and demonstration purposes since item complexity is returned by default in psych::fa. Item complexity is an indication of simple structure (i.e., items should load highly onto one factor and have weak loadings on others). Students often ask why the item complexity for particular item is greater than 2 when only one loading is displaying for that item? The issue arises when suppressing loadings less than a certain value. The weak loadings across multiple factors is usually what is causing the complexity score to be greater than 2. To help students better understand item complexity, I wrote this function. Simply, supply the function a vector of factor loadings and it will compute item complexity.

Example complexity(c(.40, .29, .10, .03, .01, .04))

You can download the file here or source it directly from the website: source("https://lrocconi.github.io/files/software/complexity.R")

Clean Matrix

This function removes rows and columns from a correlation matrix. This is useful when performing an exploratory factor analysis using a correlation matrix and one needs to drop a variable from the analysis.

The arguments in the function include:

• matrix The name of matrix object to clean
• vars A list of variables to drop from the matrix

Example cleanMatrix(myMatrix, c(var1, var3, var7))

You can download the file here or source it directly from the website: source("https://lrocconi.github.io/files/software/cleanMatrix.R")

Relative Efficiency

This function calculates the Relative Efficiency statistic for multiply imputed variables. Relative efficiency indicates the quality of the pooled estimates. The closer to 1 the better. It is based on the fraction of missing information and the number of imputations. $RE = \frac{1}{1+FMI/m}$ See Heymans, M. W. (2019). Applied Missing Data Analysis with SPSS and (R)Studio. (formula 10.4)[https://bookdown.org/mwheymans/bookmi/measures-of-missing-data-information.html]

The function takes a returned pooled mice object of class mira. Example:
model <- with(imputed_data, lm(dv ~ iv1 + iv2 + iv3))
RE(pool(model))

You can download the file here or source it directly from the website: source("https://lrocconi.github.io/files/software/RE.R")

Pooled R-squared

This function reports summary statistics for R-squared and adjusted R-squared for a pooled multiple imputation model from mice. It reports the minimum, maximum, average, and median R-squared and adjusted R-squared values across the m imputations.

The function takes a returned pooled mice object of class mira. Example:
model <- with(imputed_data, lm(dv ~ iv1 + iv2 + iv3))
poolR2(model)

You can download the file here or source it directly from the website: source("https://lrocconi.github.io/files/software/poolR2.R")

Monte Carlo Confidence Interval for Indirect Effects

This function mcci computes Mote Carlo confidence intervals for indirect effects when performing path analysis using OLS regression. This macro is based on the discussion on inferences for indirect effects from Darlington & Hayes (2017, pp. 455-464) Regression analysis and linear models.

The arguments in the function include:

• b1 Unstandardized coefficient for direct effect
• se1 Standard error of b1
• b2 Unstandardized coefficient for moderator effect
• se2 Standard error of b2
• seed Random number seed, defaults to 3000
• digits Number of digits to round output, defaults to 4.

Each argument is required. Note: Currently only compute 95% CI.

Example mcci(.365, .066, .725, .058)

You can download the file here or source it directly from the website: source("https://lrocconi.github.io/files/software/mcci.R")

SPSS Macros

An SPSS Macro for Computing Confidence Intervals for Effect Sizes

Until recently (e.g., SPSS 27), SPSS did not compute standardized mean difference effect sizes (e.g., Cohen’s d) for users when performing an independent samples or paired samples t-tests. It currently still does not compute variance explained effect sizes (e.g., eta-squared) for these analyses. This macro computes Cohen’s d, Hedge’s g, Eta-Squared, and Omega-Squared for independent, dependent, and single sample t-tests and their confidence intervals based off of the non-central t parameter.

The arguments in the macro include:

• N1 Sample size for group 1
• N2 Sample size for group 2
• CL Confidence Level (an integer, defaults to 95)
• paired (0, 1) Indicates independent or dependent/single sample t-test (Defaults to 0 or an independent design)
• obs_t The observed t value

The macro name is !ESCI and must be called first. Values must be specified for N1 and obs_t. N2 is not required for the dependent and single sample t-tests. The paired argument is used to indicate which test you are conducting: 0 = independent and is the default, 1 = paired/dependent or single sample design. The CL argument is optional, and will default to a 95% confidence level. The CL must be indicated in whole numbers (i.e., 95 for 95% and 90 for 90%). The obs_t argument must be the last argument, the order for the rest of the arguments does not matter.

Example 99% CI for an independent samples t-test: !ESCI N1=20 N2=15 CL=99 obs_t=.87.

Example 90% CI for a dependent samples t-test: !ESCI paired=1 CL=90 N1=18 obs_t=3.126.

Example 95% CI for single-sample t-test: !ESCI N1=36 CL=95 paired=1 obs_t=2.95.

You can download the file here or source it directly from the website: insert file = "https://lrocconi.github.io/files/software/EffectSizeCI.sps".

Monte Carlo Confidence Interval for Indirect Effects

This macro computes Mote Carlo confidence intervals for indirect effects when performing path analysis using OLS regression. This macro is based on the discussion on inferences for indirect effects from Darlington & Hayes (2017, pp. 455-464) Regression analysis and linear models.

The arguments in the macro include:

• b1 Unstandardized coefficient for direct effect
• se1 Standard error of b1
• b2 Unstandardized coefficient for moderator effect
• se2 Standard error of b2
• seed Random number seed, defaults to 3000.

The macro name is !mcci and must be called first. Each argument is required.

Example !mcci b1 = .365 se1 = .066 b2 = .725 se2 = .058 seed= 12345.

You can download the file here or source it directly from the website: insert file = "https://lrocconi.github.io/files/software/MonteCarloCI.sps".