Zero-Order Correlations — zero_order

Estimate zero-order correlations for any type of data. Note zero-order refers to the fact that no variables are controlled for (i.e., bivariate correlations). To our knowledge, this is the only Bayesian implementation in R that can estiamte Pearson's, tetrachoric (binary), polychoric (ordinal with more than two cateogries), and rank based correlation coefficients.

Usage

zero_order_cors(
  Y,
  type = "continuous",
  iter = 5000,
  mixed_type = NULL,
  progress = TRUE
)

Arguments

Y: Matrix (or data frame) of dimensions n (observations) by p (variables).
type: Character string. Which type of data for Y ? The options include continuous, binary, ordinal, or mixed. See the note for further details.
iter: Number of iterations (posterior samples; defaults to 5000).
mixed_type: Numeric vector. An indicator of length p for which varibles should be treated as ranks. (1 for rank and 0 to assume normality). The default is currently to treat all integer variables as ranks when type = "mixed" and NULL otherwise. See note for further details.
progress: Logical. Should a progress bar be included (defaults to TRUE) ?

Value

R An array including the correlation matrices (of dimensions p by p by iter)
R_mean Posterior mean of the correlations (of dimensions p by p)

Details

Mixed Type:

The term "mixed" is somewhat of a misnomer, because the method can be used for data including only continuous or only discrete variables. This is based on the ranked likelihood which requires sampling the ranks for each variable (i.e., the data is not merely transformed to ranks). This is computationally expensive when there are many levels. For example, with continuous data, there are as many ranks as data points!

The option mixed_type allows the user to determine which variable should be treated as ranks and the "emprical" distribution is used otherwise (Hoff 2007) . This is accomplished by specifying an indicator vector of length p. A one indicates to use the ranks, whereas a zero indicates to "ignore" that variable. By default all integer variables are treated as ranks.

Dealing with Errors:

An error is most likely to arise when type = "ordinal". The are two common errors (although still rare):

The first is due to sampling the thresholds, especially when the data is heavily skewed. This can result in an ill-defined matrix. If this occurs, we recommend to first try decreasing prior_sd (i.e., a more informative prior). If that does not work, then change the data type to type = mixed which then estimates a copula GGM (this method can be used for data containing only ordinal variable). This should work without a problem.
The second is due to how the ordinal data are categorized. For example, if the error states that the index is out of bounds, this indicates that the first category is a zero. This is not allowed, as the first category must be one. This is addressed by adding one (e.g., Y + 1) to the data matrix.

Examples

# \donttest{
# note: iter = 250 for demonstrative purposes

Y <- ptsd[,1:3]

#################################
####### example 1: Pearson's ####
#################################

fit <- zero_order_cors(Y, type = "continuous",
                       iter = 250,
                       progress = FALSE)


#################################
###### example 2: polychoric ####
#################################

fit <- zero_order_cors(Y+1, type = "ordinal",
                       iter = 250,
                       progress = FALSE)
#> Error: wishrnd(): given matrix is not symmetric positive definite


###########################
##### example 3: rank #####
###########################

fit <- zero_order_cors(Y+1, type = "mixed",
                       iter = 250,
                       progress = FALSE)

############################
## example 4: tetrachoric ##
############################

# binary data
Y <- women_math[,1:3]

fit <- zero_order_cors(Y, type = "binary",
                       iter = 250,
                       progress = FALSE)

# }