Learn the conditional (in)dependence structure with the Bayes factor using the matrix-F
prior distribution Mulder2018BGGM. These methods were introduced in
Williams2019_bf;textualBGGM. The graph is selected with select.explore and
then plotted with plot.select.
explore(
Y,
formula = NULL,
type = "continuous",
mixed_type = NULL,
analytic = FALSE,
prior_sd = 0.5,
iter = 5000,
progress = TRUE,
impute = FALSE,
seed = NULL,
...
)The returned object of class explore contains a lot of information that
is used for printing and plotting the results. For users of BGGM, the following
are the useful objects:
pcor_mat partial correltion matrix (posterior mean).
post_samp an object containing the posterior samples.
Matrix (or data frame) of dimensions n (observations) by p (variables).
An object of class formula. This allows for including
control variables in the model (i.e., ~ gender).
Character string. Which type of data for Y ? The options include continuous,
binary, ordinal, or mixed (semi-parametric copula). See the note for further details.
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 to treat all integer variables as ranks
when type = "mixed" and NULL otherwise. See note for further details.
Logical. Should the analytic solution be computed (default is FALSE)?
(currently not implemented)
Scale of the prior distribution, approximately the standard deviation of a beta distribution (defaults to 0.5).
Number of iterations (posterior samples; defaults to 5000).
Logical. Should a progress bar be included (defaults to TRUE) ?
Logicial. Should the missing values (NA)
be imputed during model fitting (defaults to TRUE) ?
An integer for the random seed.
Currently ignored (leave empty).
Controlling for Variables:
When controlling for variables, it is assumed that Y includes only
the nodes in the GGM and the control variables. Internally, only the predictors
that are included in formula are removed from Y. This is not behavior of, say,
lm, but was adopted to ensure users do not have to write out each variable that
should be included in the GGM. An example is provided below.
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. 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 handled 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.
Imputing Missing Values:
Missing values are imputed with the approach described in hoff2009first;textualBGGM.
The basic idea is to impute the missing values with the respective posterior pedictive distribution,
given the observed data, as the model is being estimated. Note that the default is TRUE,
but this ignored when there are no missing values. If set to FALSE, and there are missing
values, list-wise deletion is performed with na.omit.
# \donttest{
# note: iter = 250 for demonstrative purposes
###########################
### example 1: binary ####
###########################
Y <- women_math[1:500,]
# fit model
fit <- explore(Y, type = "binary",
iter = 250,
progress = FALSE)
# summarize the partial correlations
summ <- summary(fit)
# plot the summary
plt_summ <- plot(summary(fit))
# select the graph
E <- select(fit)
# plot the selected graph
plt_E <- plot(E)
plt_E$plt_alt
# }
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