Effect of Dropout on the Efficiency of Ds - Optimal Designs for Linear Mixed Models

Optimal designs are a class of experimental designs that are efficient with respect to some statistical criterion. Two types of optimal designs are considered in the study. D-optimal designs are designs that minimize the generalized variance of a model’s estimated parameters. Ds-optimal designs are a class of D-optimal experimental designs that are useful when the researcher is interested in estimating a subset of parameters in a given model. For a specific parameter, Ds-optimal designs would be more efficient than D-optimal designs. Although the loss in efficiency of D-optimal designs relative to Ds-optimal designs have been examined in the past literature, past research did not consider the cases where there are missing observations. Given that missing observations are ubiquitous in longitudinal studies due to dropout, the current study examines the loss in efficiency when D-optimal designs are used instead of Ds-optimal designs for data with missing observations. Results indicate that in general, location of Ds-optimal design points with dropout will shift closer towards the location of the D-optimal designs with complete data, compared to D-optimal design points with dropout. The D-optimal design with complete data corresponds with the smallest variance covariance matrix. For the data with dropout, the variance covariance matrix of the Ds-optimal design is closer in size to that of D-optimal design with complete data compared to that of D-optimal design with dropout. For both designs with dropout, efficiency loss is moderate

Planned Missing Data Designs & Small Sample Size: How Small is Too Small?

Utilizing planned missing data (PMD) designs (ex. 3-form surveys) enables researchers to ask participants fewer questions during the data collection process. An important question, however, is just how few participants are needed to effectively employ planned missing data designs in research studies. This paper explores this question by using simulated three-form planned missing data to assess analytic model convergence, parameter estimate bias, standard error bias, mean squared error (MSE), and relative efficiency (RE).Three models were examined: a one-time point, cross-sectional model with 3 constructs; a two-time point model with 3 constructs at each time point; and a three-time point, mediation model with 3 constructs over three time points. Both full-information maximum likelihood (FIML) and multiple imputation (MI) were used to handle the missing data. Models were found to meet convergence rate and acceptable bias criteria with FIML at smaller sample sizes than with MI