201_pca.Rmd

# (PART\*)  Data Reduction {-}

# Principal Component Analysis

<!-- Discussion of the model goes here -->

```{r}

pca <- function(data, scale=T, center=T) {
  
  data <- data[complete.cases(data),]
  
  if (center) mat <- apply(data, 2, function(x) x - mean(x)) else mat <- data
  if (scale) for(i in 1:ncol(mat)) mat[,i] <- mat[,i] / sd(data[,i])
  
  decomp <- svd(mat)
  var <- (decomp$d^2)/(nrow(mat)-1)
  loadings <- decomp$v
  
  colnames(loadings) <- paste0("PC", 1:ncol(loadings))
  rownames(loadings) <- colnames(mat)
  
  return(list(var=var, loadings=loadings))
  
}


```

Testing the function:

```{r}

# Dataset of English constituency vote shares from UK GE2019
library(parlitools)
df <- subset(bes_2019, 
             subset=bes_2019$country=="England",
             select=c("con_19", "lab_19", "ld_19", "brexit_19", "green_19", "other_19"))
df <- apply(df, 2, function(x) ifelse(is.na(x), 0, x))


# With centering and rescaling
pc <- prcomp(df, scale.=T)
pc$sdev^2
pc$rotation

pca(df)


# Without centering and rescaling
pc <- prcomp(df, center=F, scale.=F)
pc$sdev^2
pc$rotation

pca(df, center=F, scale=F)



```