Given the scope of large-scale assessment programs such as TIMSS, PIRLS and PISA, innovative assessment designs are needed to ensure maximum content coverage while minimizing the exam burden for any particular student. Matrix sampling of items is commonly used to measure the wide content domain and to ensure that each examinee is administered a sufficient number of items to accurately estimate proficiency distributions while minimizing individual testing time. Under these designs, students are administered just a small subset of the available items (Beaton & Zwick, 1992; Johnson, 1992), resulting in a sparse response matrix that poses challenges for estimating student proficiency. Plausible value methods (Mislevy, 1991; Mislevy, Beaton, Kaplan & Sheehan, 1992; Mislevy, Johnson & Muraki, 1992) are a common approach for generating proficiency estimates; however, proficiency and item parameter estimates are influenced by the sparseness of the response matrix and sample size. The current paper seeks to empirically investigate the degree to which person and item parameters are recovered as a function of matrix sparseness and sample size when different scaling and proficiency estimation methods are used under an incomplete matrix design. To explore this issue, we simulate data according to several matrix sample designs with varying sparseness and sample sizes, calibrate the items, and obtain proficiency estimates with several approaches.