# A. Data handling

    # Start the HDANOVA R package
    library(HDANOVA)
    #> Registered S3 method overwritten by 'lme4':
    #>   method           from
    #>   na.action.merMod car
    #>
    #> Attaching package: 'HDANOVA'
    #> The following object is masked from 'package:stats':
    #>
    #>     loadings

# Read from file

Data are stored in many different file formats. The following three examples cover two types of CSV-files and generic flat files.

    # Find directory extdata from the multiblock package
    mbdir <- system.file('extdata/', package = "multiblock")

    # Comma separated values, row names in first column
    meta_data <- read.csv(paste0(mbdir, "/meta_data.csv"), row.names = 1)
    # If working directory matches file location:
    # meta_data <- read.csv('meta_data.csv', row.names = 1)
    meta_data
    #>         temperature colour
    #> John           38.0   blue
    #> Julia          37.0  green
    #> James          37.5   blue
    #> Jacob          37.6    red
    #> Jane           37.2    red
    #> Johanna        37.9  green

    # Semi-colon separated values (locales where the decimal point is comma),
    # no row names
    proteins <- read.csv2(paste0(mbdir, "/proteins.csv"))
    proteins
    #>         prot1       prot2      prot3
    #> 1  0.46532048  0.30183300 -1.4654414
    #> 2 -1.79802081 -0.22812232 -0.4639203
    #> 3 -1.92962434 -0.40513080  0.1767796
    #> 4  0.87437138  0.79843798  0.1234731
    #> 5 -0.62445278 -0.07975479 -1.1126332
    #> 6 -0.07493721  1.09576027  1.2656596

    # Blank space separated data without labels
    genes <- read.table(paste0(mbdir, "/genes.dat"))
    genes
    #>            V1         V2         V3
    #> 1  0.39033106 -0.5720390  1.9147573
    #> 2  0.55352785  0.0948703 -0.2239755
    #> 3  0.09872346 -0.1029385  0.9047138
    #> 4 -0.59213740 -0.6027739  0.6177083
    #> 5 -0.02350148  0.3572809 -0.5168416
    #> 6  0.76644845  1.2863428  1.8239298

# Data pre-processing

Before analysis, various types of pre-processing may be needed. Centring and standardising/scaling may be considered the most basic. In R, these operations are performed column-wise by default, leading to autoscaling. If these operations are performed on the rows, we perform the standard normal variate (SNV) instead.

    # Column-centring
    genes_centred <- scale(genes, scale=FALSE)
    colMeans(genes_centred) # Check mean values
    #>           V1           V2           V3
    #> 1.850372e-17 0.000000e+00 7.401487e-17

    # Autoscaling
    genes_scaled <- scale(genes)
    apply(genes_scaled, 2, sd) # Check standard deviations
    #> V1 V2 V3
    #>  1  1  1

    # SNV (transpose, autoscale, re-transpose)
    genes_snv <- t(scale(t(genes)))
    apply(genes_snv, 1, sd) # Check standard deviations
    #> [1] 1 1 1 1 1 1

## Re-coding categorical data

Most analysis methods require continuous input data. The meta_data data.frame contains a character vector (a factor in older R versions) of categories. This package has a function dummycode for converting categorical data to various dummy formats.

    # Default is sum-coding
    dummycode(meta_data$colour)
    #>   x1 x2
    #> 1  1  0
    #> 2  0  1
    #> 3  1  0
    #> 4 -1 -1
    #> 5 -1 -1
    #> 6  0  1

    # Treatment coding
    dummycode(meta_data$colour, "contr.treatment")
    #>   xgreen xred
    #> 1      0    0
    #> 2      1    0
    #> 3      0    0
    #> 4      0    1
    #> 5      0    1
    #> 6      1    0

    # Full dummy-coding (rank deficient)
    dummycode(meta_data$colour, drop = FALSE)
    #>   xblue xgreen xred
    #> 1     1      0    0
    #> 2     0      1    0
    #> 3     1      0    0
    #> 4     0      0    1
    #> 5     0      0    1
    #> 6     0      1    0

    # Replace categorical with dummy-coded, use I() to index by common name
    meta_data2 <- meta_data
    meta_data2$colour <- I(dummycode(meta_data$colour, drop = FALSE))
    meta_data2
    #>         temperature colour.xblue colour.xgreen colour.xred
    #> John           38.0            1             0           0
    #> Julia          37.0            0             1           0
    #> James          37.5            1             0           0
    #> Jacob          37.6            0             0           1
    #> Jane           37.2            0             0           1
    #> Johanna        37.9            0             1           0
    meta_data2$colour
    #>   xblue xgreen xred
    #> 1     1      0    0
    #> 2     0      1    0
    #> 3     1      0    0
    #> 4     0      0    1
    #> 5     0      0    1
    #> 6     0      1    0

# Data structures for analysis including blocks

## Create list of blocks

A simple list of blocks can be created using the list() function. Naming of the blocks can be done directly or after creation.

    # Direct approach
    blocks1 <- list(meta = meta_data2, proteins = proteins, genes = genes)

    # Two-step approach
    blocks2 <- list(meta_data2, proteins, genes)
    names(blocks2) <- c('meta', 'proteins', 'genes')

    # Same result
    identical(blocks1, blocks2)
    #> [1] TRUE

    # Access by name or number
    blocks1[['meta']]
    #>         temperature colour.xblue colour.xgreen colour.xred
    #> John           38.0            1             0           0
    #> Julia          37.0            0             1           0
    #> James          37.5            1             0           0
    #> Jacob          37.6            0             0           1
    #> Jane           37.2            0             0           1
    #> Johanna        37.9            0             1           0
    blocks2[[1]]
    #>         temperature colour.xblue colour.xgreen colour.xred
    #> John           38.0            1             0           0
    #> Julia          37.0            0             1           0
    #> James          37.5            1             0           0
    #> Jacob          37.6            0             0           1
    #> Jane           37.2            0             0           1
    #> Johanna        37.9            0             1           0

## Create data.frame of blocks

A data.frame is a convenient storage format for data in R and can handle many types of variables, e.g. numeric, logical, character, factor or matrices. The latter is useful for analyses of data with shared sample mode.

    # Construct block data.frame from list
    df1 <- block.data.frame(blocks1)

    # Construct block data.frame from data.frame:
    # First merge blocks into data.frame
    my_data <- cbind(meta_data2, proteins, genes)
    # Then construct block data.frame using named
    # list of indexes
    df2 <- block.data.frame(my_data, block_inds =
            list(meta = 1:2, proteins = 3:5, genes = 6:8))

    # Same result
    identical(df1,df2)
    #> [1] TRUE

    # Access by name or number
    df1[[2]]
    #>               prot1       prot2      prot3
    #> John     0.46532048  0.30183300 -1.4654414
    #> Julia   -1.79802081 -0.22812232 -0.4639203
    #> James   -1.92962434 -0.40513080  0.1767796
    #> Jacob    0.87437138  0.79843798  0.1234731
    #> Jane    -0.62445278 -0.07975479 -1.1126332
    #> Johanna -0.07493721  1.09576027  1.2656596
    df2[['proteins']]
    #>               prot1       prot2      prot3
    #> John     0.46532048  0.30183300 -1.4654414
    #> Julia   -1.79802081 -0.22812232 -0.4639203
    #> James   -1.92962434 -0.40513080  0.1767796
    #> Jacob    0.87437138  0.79843798  0.1234731
    #> Jane    -0.62445278 -0.07975479 -1.1126332
    #> Johanna -0.07493721  1.09576027  1.2656596
    df1[c(1,3)]
    #>         meta.temperature meta.colour.xblue meta.colour.xgreen meta.colour.xred
    #> John                38.0               1.0                0.0              0.0
    #> Julia               37.0               0.0                1.0              0.0
    #> James               37.5               1.0                0.0              0.0
    #> Jacob               37.6               0.0                0.0              1.0
    #> Jane                37.2               0.0                0.0              1.0
    #> Johanna             37.9               0.0                1.0              0.0
    #>            genes.V1    genes.V2    genes.V3
    #> John     0.39033106 -0.57203901  1.91475732
    #> Julia    0.55352785  0.09487030 -0.22397553
    #> James    0.09872346 -0.10293847  0.90471382
    #> Jacob   -0.59213740 -0.60277392  0.61770832
    #> Jane    -0.02350148  0.35728086 -0.51684156
    #> Johanna  0.76644845  1.28634283  1.82392983
    df1[-2]
    #>         meta.temperature meta.colour.xblue meta.colour.xgreen meta.colour.xred
    #> John                38.0               1.0                0.0              0.0
    #> Julia               37.0               0.0                1.0              0.0
    #> James               37.5               1.0                0.0              0.0
    #> Jacob               37.6               0.0                0.0              1.0
    #> Jane                37.2               0.0                0.0              1.0
    #> Johanna             37.9               0.0                1.0              0.0
    #>            genes.V1    genes.V2    genes.V3
    #> John     0.39033106 -0.57203901  1.91475732
    #> Julia    0.55352785  0.09487030 -0.22397553
    #> James    0.09872346 -0.10293847  0.90471382
    #> Jacob   -0.59213740 -0.60277392  0.61770832
    #> Jane    -0.02350148  0.35728086 -0.51684156
    #> Johanna  0.76644845  1.28634283  1.82392983
    df2[c('proteins','genes')]
    #>         proteins.prot1 proteins.prot2 proteins.prot3    genes.V1    genes.V2
    #> John        0.46532048     0.30183300    -1.46544136  0.39033106 -0.57203901
    #> Julia      -1.79802081    -0.22812232    -0.46392027  0.55352785  0.09487030
    #> James      -1.92962434    -0.40513080     0.17677963  0.09872346 -0.10293847
    #> Jacob       0.87437138     0.79843798     0.12347308 -0.59213740 -0.60277392
    #> Jane       -0.62445278    -0.07975479    -1.11263323 -0.02350148  0.35728086
    #> Johanna    -0.07493721     1.09576027     1.26565956  0.76644845  1.28634283
    #>            genes.V3
    #> John     1.91475732
    #> Julia   -0.22397553
    #> James    0.90471382
    #> Jacob    0.61770832
    #> Jane    -0.51684156
    #> Johanna  1.82392983

    # Use with formula interface (see other vignettes)
    # sopls(meta ~ proteins + genes, data = df1)

    # Use with single list interface (see other vignettes)
    # mfa(df1[c(1,3)], ncomp = 3)