Multiple Imputation in Mplus

• Data set containing scores from 480 employees on eight workrelated
variables
• Variables: Age, gender, job tenure, IQ, psychological wellbeing,
job satisfaction, job performance, and turnover intentions
• 33% of the cases have missing well-being scores, and 33%
have missing satisfaction scores
• The mechanism is MCAR because the data are missing by
design

• With some planning, the same set of imputations can serve as
input data for many different analyses
• At a minimum, the imputation process should include all effects
that are of interest in the subsequent analysis phase (e.g., main
effects, interactions, non-linear relations)
• Imputation should also incorporate auxiliary variables that
predict missingness or are correlated with the analysis variables

• TITLE (optional)
• DATA (same as ML analysis)
• VARIABLE (same as ML analysis)
• ANALYSIS
• DATA IMPUTATION
• OUTPUT

• Specification with full file path
DATA:!
! Location of the data file;!
file = ‘c:\Data\employee.dat’;!
• Simplified specification when the data file and the Mplus syntax
file are located in the same folder
DATA:!
! Location of the data file;!
file = employee.dat;!

• All variables listed on the USEVARIABLES command are included
in the imputation process
• The USEVARIABLES list typically includes complete and
incomplete variables
VARIABLE:!
! Information about the contents of the data file;!
names = id age tenure female wbeing jobsat jobperf
turnover iq;!
usevariables = jobperf tenure wbeing jobsat turnover iq;!
missing = all (-99);!

• The following commands apply to the final MCMC run that
generates the imputed data sets
ANALYSIS:!
! Saturated imputation model;!
type = basic;!
! Random number seed for MCMC algorithm;!
bseed = 48932;!
! Convergence criterion (default = .05);!
bconvergence = .05;!

• Specifies characteristics of the imputation algorithm
• This command is unnecessary in the preliminary diagnostic run
DATA IMPUTATION:!
! Variables to be imputed; !
impute = wbeing jobsat;!
! Number of imputed data sets;!
ndatasets = 50;!
! File name prefix for imputed data sets;!
save = employeeimp*.dat;!
! Between-imputation interval;!
thin = 300;!

• The TECH8 option of the OUTPUT command computes the PSR
statistic after every 100 MCMC iterations and prints the values
to the output file
OUTPUT:!
! Tech8 gives the PSR statistic; !
tech8;!

DATA:!
file = employee.dat;!
VARIABLE:!
names = id age tenure female wbeing jobsat jobperf turnover iq;!
usevariables = jobperf tenure wbeing jobsat turnover iq;!
missing = all (-99);!
ANALYSIS:!
type = basic;!
bseed = 48932;!
bconvergence = .05;!
DATA IMPUTATION:!
impute = wbeing jobsat;!
ndatasets = 50;!
save = employeeimp*.dat;!
thin = 300;!
OUTPUT:!
tech8;!
!
!
!

• Near the bottom of the output file, Mplus lists the variable order
in the imputed data sets
• Use this variable list for all subsequent analyses
SAVEDATA INFORMATION!
!
Order of variables!
!
JOBPERF!
TENURE!
WBEING!
JOBSAT!
TURNOVER!
IQ!

• Mplus saves each
imputed data set to a
separate file
• The file names use the
prefix specified in the
SAVE command (e.g.,
employeeimp1.dat,
employeeimp2.dat,
employeeimp3.dat,
etc.)

• The imputation
program also
generates a list file
that contains the file
names of the imputed
data sets (e.g.,
employeeimplist.dat)
• The list file serves as
input data for all
subsequent analyses

• Mplus fully automates the analysis and pooling phases
• Analyzing imputed data sets requires a small change to the
DATA command, but the remaining commands are identical to
an ML analysis
• There is no need to list the variances and covariances for
incomplete explanatory variables because these variables are
now complete

DATA:!
file = employeeimplist.dat;
type = imputation;
! List of imputation file names;!
! Imputation data;!
VARIABLE:!
names = jobperf tenure wbeing jobsat turnover iq;!
usevariables = jobperf tenure wbeing jobsat turnover;!
missing = all (-99);!
centering = grandmean(tenure wbeing jobsat);!
ANALYSIS:!
estimator = ml;!
MODEL:!
jobperf on wbeing (b1);!
jobperf on jobsat (b2);!
jobperf on tenure (b3);!
jobperf on turnover (b4);!
MODEL TEST:!
b1 = 0; b2 = 0; b3 = 0; b4 = 0;!
OUTPUT:!
standardized sampstat patterns;!
!
!
!
!

SAMPLE STATISTICS!
!
NOTE: These are average results over 50 data sets.!
!
!
!
SAMPLE STATISTICS!
Means!
JOBPERF TENURE WBEING JOBSAT TURNOVER!
________ ________ ________ ________ ________!
1 6.021 0.000 0.000 0.000 0.321!
Covariances!
JOBPERF TENURE WBEING JOBSAT TURNOVER!
________ ________ ________ ________ ________!
JOBPERF 1.570!
TENURE 0.061 9.735!
WBEING 0.661 0.565 1.377!
JOBSAT 0.272 0.552 0.447 1.394!
TURNOVER -0.203 0.016 -0.148 -0.129 0.218!

!
!Correlations!
JOBPERF TENURE WBEING JOBSAT TURNOVER!
________ ________ ________ ________ ________!
JOBPERF 1.000!
TENURE 0.016 1.000!
WBEING 0.450 0.154 1.000!
JOBSAT 0.184 0.150 0.323 1.000!
TURNOVER -0.346 0.011 -0.269 -0.235 1.000!

• The Wald statistic (a chi-square with 4 degrees of freedom) is
akin to the omnibus F test in OLS regression
Wald Test of Parameter Constraints!
!
Value 177.808!
Degrees of Freedom 4!
P-Value 0.0000!
• The significant chi-square, χ 2 (4)= 177.808, p < .001, indicates
that the set of predictors explain significant variation in the
dependent variable

!
!
MODEL RESULTS!
!
Unstandardized
Coefficients
Standard
Error
z Test
Two-Tailed!
Estimate S.E. Est./S.E. P-Value!
!
JOBPERF ON!
WBEING 0.417 0.057 7.366 0.000!
JOBSAT 0.009 0.053 0.170 0.865!
TENURE -0.017 0.017 -1.034 0.301!
TURNOVER -0.640 0.116 -5.522 0.000!
!
Intercepts!
JOBPERF 6.226 0.062 100.981 0.000!

• Because the continuous are centered at their means, the
intercept estimate (B 0 = 6.226) represents the adjusted mean
for the group of employees that intend to stay on the job
(TURNOVER = 0)
• Controlling for other variables, employees that intend to quit
(TURNOVER = 1) have a .640 lower job performance mean (B 4
= -.640, p < .001)
• Holding other variables constant, one-point increase in wellbeing
would produce a .417 increase in job performance, on
average (B 1 = .417, p < .001)

!
STANDARDIZED MODEL RESULTS!
!
!
STDYX Standardization!
!
JOBPERF ON!
Beta
Weights
Two-Tailed!
Estimate S.E. Est./S.E. P-Value!
WBEING 0.390 0.051 7.720 0.000!
JOBSAT 0.009 0.050 0.170 0.865!
TENURE -0.043 0.042 -1.035 0.301!
TURNOVER -0.238 0.042 -5.631 0.000!

!
R-SQUARE!
!
!
Observed
Two-Tailed!
Variable Estimate S.E. Est./S.E. P-Value!
JOBPERF 0.260 0.040 6.568 0.000!

• Prior to performing the analyses, we used multiple imputation to
deal with the missing data. Briefly, multiple imputation uses a
regression-based procedure to generate multiple copies of the
data set, each of which contains different estimates of the missing
values. We used the fully conditional specification algorithm in the
SPSS multiple imputation procedure to generate 50 imputed data
sets. An exploratory analysis suggested that the data sets should
be separated by at least 100 iterations, so we took a conservative
approach of saving a data set after every 300 th computational
cycle. The imputation model included the five regression model
parameters and IQ scores.

• After creating the complete data sets, we estimated the multiple
regression model on each filled-in data set and subsequently
used Rubin’s (1987) formulas to combine the parameter
estimates and standard errors into a single set of results. Note
that methodologists currently regard multiple imputation as a
“state of the art” missing data technique (Schafer & Graham,
2002) because it requires less strict assumptions about the
mechanism that led to missing data and generally produces
more accurate estimates than traditional missing data handling
techniques (e.g., discarding cases).

• Considered as a set, the four predictors explained approximately
26% of the variability in job performance scores, R 2 = .26. Table 1
gives the regression coefficients from the analysis. Because the
continuous predictors were centered at their means, the intercept
quantifies the average job performance rating for employees that
intend to stay in their current position. As seen in the table,
psychological well-being was a significant predictors of job
performance, such that one-point increase in well-being scores was
associated with a .417 increase in job performance, controlling for
other predictors, z = 7.336, p < .001. Turnover intentions was also a
significant unique predictor, such that employees with intentions to quit
had a .64 lower job performance average after controlling for other
predictors, t = -5.522, p < .001.

• Tabular presentations of missing data analyses are identical to
those from a complete-data analysis
Table 1
Multiple Regression Parameter Estimates
Effect Est. Beta SE z p
Intercept 6.226 N/A .062 100.981 < .001
Well-Being .417 .390 .057 7.336 < .001
Job Satisfaction .009 .009 .053 .170 .865
Job Tenure -.017 -.043 .017 -1.034 .301
Turnover Intentions -.640 -2.238 .116 -5.522 < .001