Comparative Analysis of Microbiome Measurement Platforms Using Latent Variable Structural
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Comparative Analysis of Microbiome Measurement Platforms
Using Latent Variable Structural Equation Modeling
Xiao Wu1, Kathryn Berkow1, Daniel N. Frank2, Ellen Li3,4, Ajay S. Gulati5, Wei Zhu1
1Department of Applied Mathematics and Statistics, Stony Brook University, Stony
Brook, NY; 2Division of Infectious Diseases, University of Colorado Anschutz Medical
Campus, Aurora, CO; 3Department of Medicine, Stony Brook University, Stony Brook,
NY; 4Department of Medicine, Washington University, St. Louis, MO. 5Department of
Pediatrics, University of North Carolina, Chapel Hill, NC.
1 SUPPLEMENTARY MATERIALS
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).
(A) Proteobacteria
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
(B) Firmicutes/Clostridia/Clostridiales/LachnoIV
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
(C) Actinobacteria
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
(D) Bacteroidetes
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
2 (E) Firmicutes/Bacilli
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
Text S1. Reliability in the measurement model of latent variable SEM
For the latent SEM model illustrated in Figure 1(A), we have:
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 )
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 .
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