title: On the Asymptotic Relative Efficiency of Planned Missingness Designs.
abstract: In planned missingness (PM) designs, certain data are set a priori to be missing. PM designs can increase validity and reduce cost; however, little is known about the loss of efficiency that accompanies these designs. The present paper compares PM designs to reduced sample (RN) designs that have the same total number of data points concentrated in fewer participants. In 4 studies, we consider models for both observed and latent variables, designs that do or do not include an "X set" of variables with complete data, and a full range of between- and within-set correlation values. All results are obtained using asymptotic relative efficiency formulas, and thus no data are generated; this novel approach allows us to examine whether PM designs have theoretical advantages over RN designs removing the impact of sampling error. Our primary findings are that (a) in manifest variable regression models, estimates of regression coefficients have much lower relative efficiency in PM designs as compared to RN designs, (b) relative efficiency of factor correlation or latent regression coefficient estimates is maximized when the indicators of each latent variable come from different sets, and (c) the addition of an X set improves efficiency in manifest variable regression models only for the parameters that directly involve the X-set variables, but it substantially improves efficiency of most parameters in latent variable models. We conclude that PM designs can be beneficial when the model of interest is a latent variable model; recommendations are made for how to optimize such a design.
authors.affiliation: Programme Group Psychological Methods, Department of Psychology, University of Amsterdam, Weesperplein 4, Room 208, 1018XA, Amsterdam, Netherlands. m.rhemtulla@uva.nl.
authors.forename: Mijke
authors.initials: M
authors.lastname: Rhemtulla
authors.affiliation: Department of Psychology, University of British Columbia, 3410-2136 West Mall, Vancouver, BC, V6T 1Z4, Canada. v.savalei@ubc.ca.
authors.forename: Victoria
authors.initials: V
authors.lastname: Savalei
authors.affiliation: Department of Educational Psychology and Leadership, College of Education, Texas Tech University, Box 40171, Lubbock, TX, 79409, USA. todd.d.little@ttu.edu.
authors.forename: Todd D
authors.initials: TD
authors.lastname: Little
mesh_terms: D003627:Data Interpretation, Statistical; D015233:Models, Statistical; D011594:Psychometrics
keywords: efficiency; incomplete data; missing data; missingness by design; planned missing; power