<p>Comparative Analysis of Microbiome Measurement Platforms</p><p>Using Latent Variable Structural Equation Modeling</p><p>Xiao Wu1, Kathryn Berkow1, Daniel N. Frank2, Ellen Li3,4, Ajay S. Gulati5, Wei Zhu1</p><p>1Department of Applied Mathematics and Statistics, Stony Brook University, Stony</p><p>Brook, NY; 2Division of Infectious Diseases, University of Colorado Anschutz Medical</p><p>Campus, Aurora, CO; 3Department of Medicine, Stony Brook University, Stony Brook,</p><p>NY; 4Department of Medicine, Washington University, St. Louis, MO. 5Department of</p><p>Pediatrics, University of North Carolina, Chapel Hill, NC.</p><p>1 SUPPLEMENTARY MATERIALS</p><p>Table S1. Pearson correlations between three different measurements (Sanger, 454_V1V3 and 454_V3V5) of various bacterial taxa. Bacterial relative frequencies were logit transformed (N = 142). </p><p>(A) Proteobacteria</p><p>454_V1V3 454_V3V5 Pearson Correlation Sanger (p value) (p value) 0.649 0.800 Sanger 1 (<.001) (<.001) 0.790 454_V1V3 1 (<.001) 454_V3V5 1</p><p>(B) Firmicutes/Clostridia/Clostridiales/LachnoIV</p><p>454_V1V3 454_V3V5 Pearson Correlation Sanger (p value) (p value) 0.795 0.737 Sanger 1 (<.001) (<.001) 0.855 454_V1V3 1 (<.001) 454_V3V5 1</p><p>(C) Actinobacteria</p><p>454_V1V3 454_V3V5 Pearson Correlation Sanger (p value) (p value) 0.705 0. 717 Sanger 1 (<.001) (<.001) 0. 868 454_V1V3 1 (<.001) 454_V3V5 1</p><p>(D) Bacteroidetes</p><p>454_V1V3 454_V3V5 Pearson Correlation Sanger (p value) (p value) 0.753 0.819 Sanger 1 (<.001) (<.001) 0.901 454_V1V3 1 (<.001) 454_V3V5 1</p><p>2 (E) Firmicutes/Bacilli</p><p>454_V1V3 454_V3V5 Pearson Correlation Sanger (p value) (p value) 0.816 0.818 Sanger 1 (<.001) (<.001) 0.956 454_V1V3 1 (<.001) 454_V3V5 1</p><p>Text S1. Reliability in the measurement model of latent variable SEM</p><p>For the latent SEM model illustrated in Figure 1(A), we have:</p><p>R2= r 2 (squared correlation between observed and latent variable) yi y i ,x 2 2 cov (yi ,x ) cov ( l i x+ e i , x ) = =(Q yi =l i x + e i ) Var( yi ) Var (x ) Var ( l i x+ e i ) Var ( x ) 2 [liVar ( x )+ cov( e i , x )] = 2 [liVar ( x )+ cov( l i x , e i ) + Var ( e i )] Var ( x ) 2 [liVar(x )] = 2 (Q ei^ x ,cov( e i , x ) = 0) [liVar ( x )+ Var ( e i )] Var ( x ) 2 2 liVar( x ) l i Var ( x ) Var ( l i x ) Var ( e i ) =2 = = =1 - liVar( x )+ Var ( e i ) Var ( y i ) Var ( y i ) Var ( y i )</p><p>The last term in the equation can be interpreted as the proportion of variance in the measure Y i that is explained by the latent variablex . </p><p>3</p>