3-Form Planned Missing Data Designs for Personality and Social Psychology
Graham G. Rifenbark, Alexander M. Schoemann, Wei Wu, & Todd D. Little
3-Form Planned Missing Design
Model
 Items are split into 4 groups (X block, A block, B block and C
block)
 Participants are randomly placed into one of three conditions,
where all participants answer survey items from the X block and
two other forms: A&B; B&C; or A&C.
 It is best to split scale items across all forms to ensure appropriate
coverage.
 The missingness created by the omitted form can be described as
Missing Completely at Random (MCAR). This mechanism of
missingness allows for unbiased estimation of the model’s
parameters estimates.
Form
1/3 of N
1/3 of N
1/3 of N
Set X
X
X
X
Set A
Missing
X
X
Set B
X
Missing
X
Set C
X
X
Missing
Model estimated in the simulation. Black items are in the X block, green items are in the A block, red items are in the b block and blue items are in the C block
Benefits of using the 3-Form PMD…
 Because participants are answering fewer questions, the validity
of their responses increases as the probability of fatigue
decreases (Raghunathan & Grizzle, 1995).
 Participants are less likely to be fatigued , therefore the amount
of unplanned missing data decreases. This is because fatigued
participants are more likely to skip items, which allows for the
presence of less forgivable mechanisms of missing data that can
cause the parameters to be estimated with bias.
 Since 1/3 of the observations per form have been omitted, the
cost of such a data collection decreases greatly (Graham et al.,
2006).
 Allows the researcher to ask more questions, which increases the
amount of information available.
Estimation of Missing Data
 Full Information Maximum Likelihood (FIML) was used to
estimate the missing data.
 FIML estimation is model implied, thus software uses the data
that is present to determine the most appropriate parameter
estimates. As long as all variables are included in the model or
are specified as auxiliary variables, the estimation of Missing at
Random (MAR) or MCAR will be unbiased.
Funding generously
provided by:
Simulation
 1000 datasets were generated (N = 500), based on a four factor confirmatory factor
analysis (CFA) model. Each factor had 8 indicators.
 Aside from the planned missingness; an additional 5% of MCAR was imposed.
 On average each dataset had roughly 25% missing.
 We investigated whether employing the 3-Form planned missing design allows for
unbiased estimation of parameter estimates without a significant loss of power
compared to complete data designs.
 Simulation was conducted using the R package simsem 0.4-6 (Pornprasertmanit,
Miller, & Schoemann, 2012).
 All 1000 replications converged successfully.
Results
Lambda
Theta
Psi
Tau
Average Bias 0.001
0.003
0.001
0.001
Average Bias 0.001
0.002
0.001
0.001
Average Power 1.000
1.000 0.999 - 1.000 0.038 - 0.061
Average Power 1.000
1.000
1.000
0.034 - 0.063
*Estimates represent absolute degree of bias
*Red font corresponds to results from incomplete data design
Conclusions
 As expected there was not a significant loss of power in
estimating the model, even with the missingness imposed by the
3-Form Planned Missing Data Design.
 Model parameters were estimated with minimal bias.
 The 3-Form Planned Missing Data Design would be beneficial to
Personality and Social Psychology studies.
 Using the 3-forms planned missing design can increase the
amount of data collected from each participant with a minimal
loss of power or bias.
References
Enders, C. K. (2010). Applied missing data analysis. New York, NY: Guilford Press.
Graham, J. W., Taylor, B. J., Olchowski, A. E., & Cumsille, P. E. (2006). Planned missing data designs
in psychological research. Psychological Methods, 11, 323–343.
Graham, J. W., Taylor, B. J.,& Cumsille, P. E. (2001). Planned missing data designs in the analysis of
change. In L. M. Collins & A. G. Sayer (Eds.), New methods for the analysis of change
(pp.335–353). Washington, DC: American Psychological Association.
Pornprasertmanit, S., Miller, P., & Schoemann, A. (2012). simsem: SIMulated Structural Equation
Modeling. R package version 0.4-6. http://CRAN.R-project.org/package=simsem.
R Core Team (2012). R: A language and environment for statistical computing. R Foundation for
Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org/.
Raghunathan, T. E., & Grizzle, J. E. (1995). A split questionnaire survey design. Journal of the
American Statistical Association, 90, 54-63.