Association analysis - RDA

Multivariate redundancy analysis (RDA) in 

  - Analysis of associations between data with different units

• Using z-score standardized data
• 'vegan' package
• 'rda' funtion

# Install package

library(vegan)

 

# Redating csv form data

data1 <- read.csv("C:/Users/data.csv", header=TRUE, row.names=1)

 

# Converting variable types after checking data and variable types

str(data1)

data1$Var1_1 <- as.numeric(data1$Var1)

data1$Var2_1 <- as.numeric(data1$Var2)

 

# Data separtion after checking variable name and column

colnames(data1)

data2 <- data1[,3:12] 
data3 <- data1[,13:17]
data4 <- data1[,18:25]

# Data z-score standardization  

## Centering (means~0), Scaling (standard deviations=1) 

data2_std.z <- decostand(data2 , method="standardize")
apply(data2_std.z, 2, mean)
apply(data2_std.z, 2, sd)   

data3_std.z <- decostand(data3 , method="standardize")
apply(data3_std.z, 2, mean)
apply(data3_std.z, 2, sd) 

 

# RDA

my.rda <- rda(data2_std.z ~ ., data=data3_std.z)
summary(my.rda)

 

• Interpreting results

Partitioning of variance: 

	Inertia	Proportion
Total	5.000	1.0000
Constrained	0.231	0.0462
Unconstrained	4.769	0.9538

Eigenvalues, and their contribution to the variance 

Importance of components:

	RDA1	RDA2	RDA3	PC1	PC2	PC3	PC4	PC5
Eigenvalue	0.12472	0.09552	0.010785	1.4360	1.0720	0.9243	0.8090	0.5277
Proportion Explained	0.02494	0.01910	0.002157	0.2872	0.2144	0.1849	0.1618	0.1055
Cumulative Proportion	0.02494	0.04405	0.046205	0.3334	0.5478	0.7327	0.8945	1.0000

Variables explain 0.04% of the variance;

(0.12472+0.09552) / 5.000 = 0.04405%

 

The first constrained axis (RDA1) explains 0.12472 / 5.000 = 0.025% of the variance.

The secod constrained axis (RDA2) explains 0.09552 / 5.000 = 0.019% of the variance.
 

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Receiver operating characteristic (ROC) in R

  - Validation the accuracy of the relationship

• 'pROC' package
• 'roc' funtion