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This
Rtutorial automates the 3-step ML auxiliary variable procedure using theMplusAutomationpackage (Hallquist & Wiley, 2018) to estimate models and extract relevant parameters. To learn more about auxiliary variable integration methods and why multi-step methods are necessary for producing un-biased estimates see Asparouhov & Muthén (2014).
The motivation for this tutorial is that conducting the 3-step manually is highly error prone as it requires pulling logit values estimated in the step-1 model and adding them in the model statement of the step-2 model (i.e., lots of copying & pasting). In contrast, this approach is fully replicable and provides clear documentation which translates to more reliable research. Also, it saves time!
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How to reference this tutorial:
Garber, A. C. (2021). 3-Step ML Auxiliary Variable Integration Using MplusAutomation. Retrieved from psyarxiv.com/phtxa
Follow along! Link to Github repository:
https://github.com/immerse-ucsb/3step-ML-auto
Load packages
library(MplusAutomation) # Conduit between R & Mplus
library(glue) # Pasting R code into strings
library(here) # Location, location, location
library(tidyverse) # Tidyness
library(gt) # Tables
The CRDC is a federally mandated school and district level data collection effort that occurs every other year. This public data is currently available for selected variables across 4 years (2011, 2013, 2015, 2017) and all US states. In the following tutorial six focal variables are utilized as indicators of the latent class model; three variables which report on harassment/bullying in schools based on disability, race, or sex, and three variables on full-time equivalent school staff employees (counselor, psychologist, law enforcement). For this example, we utilize a sample of schools from the state of Arizona reported in 2017.
Information about CRCD: https://www2.ed.gov/about/offices/list/ocr/data.html
Data access (R): https://github.com/UrbanInstitute/education-data-package-r
Read in CSV data file from the data subfolder
data_3step <- read_csv(here("data", "crdc_aux_data.csv"))
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Step 1 - Estimate the unconditional model with all covariate & distal outcome variables mentioned in the auxiliary statement.
NOTE: In this example, Mplus input and output files are directed to the sub-folder 3step_mplus. Due to the fact that adding auxiliary variables is conducted after enumeration, generally other sub-folders will exist in the top-most Rproject folder such as enum_mplus, data, and figures.
m_step1 <- mplusObject(
TITLE = "Step1 (MANUAL 3-STEP ML APPROACH)",
VARIABLE =
"categorical = report_dis report_race report_sex counselors_fte psych_fte law_fte;
usevar = report_dis report_race report_sex counselors_fte psych_fte law_fte;
classes = c(3);
!!! All auxiliary variables to be considered in the final model should be listed here !!!
auxiliary =
lunch_program read_test math_test;",
ANALYSIS =
"estimator = mlr;
type = mixture;
starts = 500 100;
!!! to replicate class order use, `optseed = 887580;` !!!",
SAVEDATA =
"!!! This saved dataset will contain class probabilities and modal assignment columns !!!
File=3step_savedata.dat;
Save=cprob;
Missflag= 999;",
PLOT =
"type = plot3;
series = report_dis report_race report_sex counselors_fte psych_fte law_fte(*);",
usevariables = colnames(data_3step),
rdata = data_3step)
m_step1_fit <- mplusModeler(m_step1,
dataout=here("3step_mplus", "Step1_3step.dat"),
modelout=here("3step_mplus", "Step1_3step.inp") ,
check=TRUE, run = TRUE, hashfilename = FALSE)
Extract logits for the classification probabilities for the most likely latent class
logit_cprobs <- as.data.frame(m_step1_fit[["results"]]
[["class_counts"]]
[["logitProbs.mostLikely"]])
Extract saved data from the step 1 model mplusObject named "m_step1_fit"
savedata <- as.data.frame(m_step1_fit[["results"]]
[["savedata"]])
Rename the column in savedata for "C" and change to "N"
colnames(savedata)[colnames(savedata)=="C"] <- "N"
This model is estimated to check that the class proportions are approximately the same as in step 1.
m_step2 <- mplusObject(
TITLE = "Step2 (MANUAL 3-STEP ML APPROACH)",
VARIABLE =
"nominal=N;
USEVAR = n;
missing are all (999);
classes = c(3); ",
ANALYSIS =
"estimator = mlr;
type = mixture;
starts = 0;",
MODEL =
glue(
"%C#1%
[n#1@{logit_cprobs[1,1]}];
[n#2@{logit_cprobs[1,2]}];
%C#2%
[n#1@{logit_cprobs[2,1]}];
[n#2@{logit_cprobs[2,2]}];
%C#3%
[n#1@{logit_cprobs[3,1]}];
[n#2@{logit_cprobs[3,2]}];"),
usevariables = colnames(savedata),
rdata = savedata)
m_step2_fit <- mplusModeler(m_step2,
dataout=here("3step_mplus", "Step2_3step.dat"),
modelout=here("3step_mplus", "Step2_3step.inp"),
check=TRUE, run = TRUE, hashfilename = FALSE)
Specification details:
- This example contains two distal outcomes (
read_test&math_test) and one binary covariate (lunch_program). - Under each class-specific statement (e.g.,
%C#1%) the distal outcomes are mentioned to estimate the intercept parameters. - Moderation is specified by mentioning the
"outcome ON covariate;"syntax under each of the class-specific statements. - Note that the binary covariate is centered so that reported distal means (intercepts) are estimated at the weighted average of
lunch_program.
m_step3 <- mplusObject(
TITLE = "Step3 (MANUAL 3-STEP ML APPROACH)",
VARIABLE =
"nominal = N;
usevar = n;
missing are all (999);
usevar = lunch_pr read_tes math_tes;
classes = c(3); ",
DEFINE =
"Center lunch_pr (Grandmean);",
ANALYSIS =
"estimator = mlr;
type = mixture;
starts = 0;",
MODEL =
glue(
"!!! OUTCOMES = read_tes math_tes !!!
!!! MODERATOR = lunch_pr !!!
%OVERALL%
read_tes on lunch_pr;
read_tes;
math_tes on lunch_pr;
math_tes;
%C#1%
[n#1@{logit_cprobs[1,1]}];
[n#2@{logit_cprobs[1,2]}];
[read_tes](m01);
read_tes; !!! estimate conditional intercept !!!
read_tes on lunch_pr (s01); !!! estimate conditional regression !!!
[math_tes] (m1);
math_tes;
math_tes on lunch_pr (s1);
%C#2%
[n#1@{logit_cprobs[2,1]}];
[n#2@{logit_cprobs[2,2]}];
[read_tes](m02);
read_tes;
read_tes on lunch_pr (s02);
[math_tes] (m2);
math_tes;
math_tes on lunch_pr (s2);
%C#3%
[n#1@{logit_cprobs[3,1]}];
[n#2@{logit_cprobs[3,2]}];
[read_tes](m03);
read_tes;
read_tes on lunch_pr (s03);
[math_tes] (m3);
math_tes;
math_tes on lunch_pr (s3);"),
MODELCONSTRAINT =
"New (diff12 diff13
diff23 slope12 slope13
slope23 ndiff12 ndiff13
ndiff23 nslope12 nslope13
nslope23);
diff12 = m1-m2; ndiff12 = m01-m02;
diff13 = m1-m3; ndiff13 = m01-m03;
diff23 = m2-m3; ndiff23 = m02-m03;
slope12 = s1-s2; nslope12 = s01-s02;
slope13 = s1-s3; nslope13 = s01-s03;
slope23 = s2-s3; nslope23 = s02-s03;",
MODELTEST =
## NOTE: Only a single Wald test can be conducted per model run. Therefore,
## this example requires running separate models for each omnibus test (e.g.,
## 4 models; 2 outcomes and 2 slope coefficients). This can be done by
## commenting out all but one test and then estimating multiple versions of the model.
"!m01=m02; !!! Distal outcome omnibus Wald test for `read_tes` !!!
!m02=m03;
!s01=s02; !!! Slope difference omnibus Wald test for `read_tes on lunch_pr` !!!
!s02=s03;
m1=m2; !!! Distal outcome omnibus Wald test for `math_tes` !!!
m2=m3;
!s1=s2; !!! Slope difference omnibus Wald test `math_tes on lunch_pr` !!!
!s2=s3;
",
usevariables = colnames(savedata),
rdata = savedata)
m_step3_fit <- mplusModeler(m_step3,
dataout=here("3step_mplus", "Step3_3step.dat"),
modelout=here("3step_mplus", "Step3_3step.inp"),
check=TRUE, run = TRUE, hashfilename = FALSE)
End of 3-Step Procedure
NOTE: The next video in this series will include a detailed tutorial on how to interpret auxiliary variable output (i.e. distal outcomes & covariates) in the context of moderation. This tutorial will also cover
Rcode to generate figures for visualizing the results.
Asparouhov, T., & Muthén, B. O. (2014). Auxiliary variables in mixture modeling: Three-step approaches using Mplus. Structural Equation Modeling, 21, 329–341. http://dx.doi.org/10.1080/10705511.2014.915181
Hallquist, M. N., & Wiley, J. F. (2018). MplusAutomation: An R Package for Facilitating Large-Scale Latent Variable Analyses in Mplus. Structural equation modeling: a multidisciplinary journal, 25(4), 621-638.
Müller, Kirill. (2017). Here: A Simpler Way to Find Your Files. https://CRAN.R-project.org/package=here.
Muthén, B. O., Muthén, L. K., & Asparouhov, T. (2017). Regression and mediation analysis using Mplus. Los Angeles, CA: Muthén & Muthén.
Muthén, L.K. and Muthén, B.O. (1998-2017). Mplus User's Guide. Eighth Edition. Los Angeles, CA: Muthén & Muthén
US Department of Education Office for Civil Rights. (2014). Civil rights data collection data snapshot: School discipline. Issue brief no. 1.
R Core Team (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/
Wickham et al., (2019). Welcome to the tidyverse. Journal of Open Source Software, 4(43), 1686, https://doi.org/10.21105/joss.01686