mantar provides users with several methods for handling
missing data in the context of network analysis. Currently, these
methods are specifically implemented for network estimation via
neighborhood selection using the Bayesian Information Criterion
(BIC).
You can install the development version of mantar from GitHub with:
# install.packages("pak")
pak::pak("kai-nehler/mantar")After installation the easiest way to get an overview of functions
and capabilities is to use ?mantar to open the package
help-file. You could also read the rest of this README for an
introduction and some examples.
As already described, the package currently focuses on network estimation using neighborhood selection with information criteria for model selection in node-wise regressions. This functionality is available for both complete and incomplete data.
For datasets with missing values, two modern missing approaches are implemented:
lavaan package. It performs well when the sample size
is very large relative to the amount of missingness and the complexity
of the network.mice package. The imputed data sets are stacked into a
single data set, and a correlation matrix is estimated from this
combined data.Both methods produce a correlation matrix that is then used to estimate the network via node-wise regressions. It is also possible to compute the correlation matrix using pairwise or listwise deletion. However, these methods are generally not recommended, except in specific cases, such as when data are missing completely at random and the proportion of missingness is very small.
In addition to network estimation, the package also supports stepwise regression search based on information criteria for a single dependent variable. This regression search is available for both complete and incomplete data and relies on the same two-step EM or stacked MI procedures to handle missing values as the network analysis. While both methods to handle missingness are expected to perform well in this context, no specific simulation study has been conducted to compare their effectiveness for single regression modeling, and thus their relative strengths remain an open question.
The package includes two dummy datasets that resemble a typical psychological dataset, where the number of observations is considerably larger than the number of variables. Although the variables have descriptive names, these are included solely to make the examples more engaging - the data themselves are fully synthetic.
mantar_dummy_full: Fully observed data (no missing
values)mantar_dummy_mis: Data with missing valuesThese data sets are intended for examples and testing only.
library(mantar)
# Load example data
data(mantar_dummy_full)
data(mantar_dummy_mis)
# Preview the first few rows
head(mantar_dummy_full)
#> EmoReactivity TendWorry StressSens SelfAware Moodiness Cautious
#> 1 -0.08824641 -0.2659269 -1.2036137 -2.3499259 0.6693700 0.04102854
#> 2 -0.44657803 -0.4588384 -0.2431794 -0.1656722 -0.3361568 0.88919849
#> 3 -1.06934325 -1.5050242 -0.8986388 -1.0857552 0.2249633 0.77060142
#> 4 0.58282029 -0.5036316 -1.6020000 1.0820676 -0.1858346 -0.03462852
#> 5 0.58791759 0.5972580 -0.5882332 1.7461103 0.7160714 1.58280444
#> 6 0.10224725 0.1494428 -1.0877812 -1.7886107 1.3522197 -0.25494638
#> ThoughtFuture RespCriticism
#> 1 0.6484939 -0.77992262
#> 2 0.2949630 -0.91747608
#> 3 -1.3519007 0.56000763
#> 4 -0.4702988 0.34653985
#> 5 0.9503597 0.82981174
#> 6 -0.8938618 -0.01593388
head(mantar_dummy_mis)
#> EmoReactivity TendWorry StressSens SelfAware Moodiness Cautious
#> 1 -1.7551632 -0.4376210 -0.5774722 0.10562820 0.6614044 NA
#> 2 -1.7551688 -0.7039623 0.9070330 0.03418623 0.6140406 0.83879818
#> 3 2.0493638 NA NA NA -0.8872971 0.04830719
#> 4 0.1056282 NA NA -1.24779117 -0.7298623 -0.62263184
#> 5 -0.6338512 0.4361078 -0.5564631 -0.01032403 NA -0.09690612
#> 6 0.1054382 0.6935808 2.6557231 NA NA -0.04358574
#> ThoughtFuture RespCriticism
#> 1 0.7710993 0.37233355
#> 2 -1.5588119 -0.55079199
#> 3 NA -0.90103222
#> 4 -0.7100126 0.80773402
#> 5 1.0583312 0.20820252
#> 6 NA -0.03915726The main function for estimating a network is
neighborhood_net(). In the case of fully observed data, the
function takes the dataset as input and estimates a network structure
using neighborhood selection guided by
information criteria. With default arguments, only the
dataset needs to be provided.
The k argument controls the penalty used in model
selection for node-wise regressions. It reflects the penalty per
parameter (i.e., number of predictors + 1):
k = "log(n)" (default): corresponds to the
Bayesian Information Criterion (BIC)k = "2": corresponds to the Akaike Information
Criterion (AIC)The pcor_merge_rule argument determines how partial
correlations are estimated based on the regression results between two
nodes:
"and" (default): a partial correlation is estimated
only if both regression weights (from node A to B and
from B to A) are non-zero."or": a partial correlation is estimated if at
least one of the two regression weights is non-zero.Although both options are available, current simulation evidence
suggests that the "and" rule yields more accurate partial
correlation estimates than the "or" rule. Therefore,
changing this default is not recommended unless you
have a specific reason.
# Estimate network from full data set using BIC and and rule
result <- neighborhood_net(data = mantar_dummy_full,
k = "log(n)",
pcor_merge_rule = "and")
#> No missing values in data. Sample size for each variable is equal to the number of rows in the data.
# View estimated partial correlations
result
#> EmoReactivity TendWorry StressSens SelfAware Moodiness Cautious
#> EmoReactivity 0.0000000 0.2617524 0.130019 0.0000000 0.0000000 0.0000000
#> TendWorry 0.2617524 0.0000000 0.000000 0.2431947 0.0000000 0.0000000
#> StressSens 0.1300190 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
#> SelfAware 0.0000000 0.2431947 0.000000 0.0000000 0.0000000 0.0000000
#> Moodiness 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.4377322
#> Cautious 0.0000000 0.0000000 0.000000 0.0000000 0.4377322 0.0000000
#> ThoughtFuture 0.0000000 0.2595917 0.000000 0.0000000 0.0000000 0.0000000
#> RespCriticism 0.0000000 0.0000000 0.000000 0.0000000 0.2762595 0.2523658
#> ThoughtFuture RespCriticism
#> EmoReactivity 0.0000000 0.0000000
#> TendWorry 0.2595917 0.0000000
#> StressSens 0.0000000 0.0000000
#> SelfAware 0.0000000 0.0000000
#> Moodiness 0.0000000 0.2762595
#> Cautious 0.0000000 0.2523658
#> ThoughtFuture 0.0000000 0.0000000
#> RespCriticism 0.0000000 0.0000000
# Create and view a summary of the network estimation
sum_result <- summary(result)
sum_result
#> The density of the estimated network is 0.250
#>
#> Network was estimated using neighborhood selection with a penalty term of log(n)
#> and the 'and' rule for the inclusion of edges based on a full data set.
#>
#> The sample sizes used for the nodewise regressions were as follows:
#> EmoReactivity TendWorry StressSens SelfAware Moodiness
#> 400 400 400 400 400
#> Cautious ThoughtFuture RespCriticism
#> 400 400 400In the case of missing data, the neighborhood_net()
function offers several additional arguments that control how sample
size and missingness are handled.
The n_calc argument specifies how the sample size is
calculated for each node-wise regression. This affects the penalty term
used in model selection.
The available options are:
"individual" (default): Uses the number of
non-missing observations for each individual variable. This is the
recommended approach."average": Uses the average number of non-missing
observations across all variables."max": Uses the maximum number of non-missing
observations across all variables."total": Uses the total number of observations in the
dataset (i.e., the number of rows).The missing_handling argument specifies how the
correlation matrix is estimated when the input data contains missing
values. Two approaches are supported:
"two-step-em": Applies a classic
Expectation-Maximization (EM) algorithm to estimate the
covariance matrix."stacked-mi": Applies multiple
imputation to create several completed datasets, which are then
stacked into a single dataset. A correlation matrix is computed from
this stacked data.If "stacked-mi" is used, the nimp argument
controls the number of imputations (default: 20).
# Estimate network for data set with missing values
result_mis <- neighborhood_net(data = mantar_dummy_mis,
n_calc = "individual",
missing_handling = "two-step-em",
pcor_merge_rule = "and")
# View estimated partial correlations
result_mis
#> EmoReactivity TendWorry StressSens SelfAware Moodiness Cautious
#> EmoReactivity 0.0000000 0.1295824 0.230612 0.0000000 0.0000000 0.0000000
#> TendWorry 0.1295824 0.0000000 0.000000 0.2515697 0.0000000 0.0000000
#> StressSens 0.2306120 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
#> SelfAware 0.0000000 0.2515697 0.000000 0.0000000 0.0000000 0.0000000
#> Moodiness 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.4768098
#> Cautious 0.0000000 0.0000000 0.000000 0.0000000 0.4768098 0.0000000
#> ThoughtFuture 0.1446363 0.2991518 0.000000 0.0000000 0.0000000 0.0000000
#> RespCriticism 0.0000000 0.0000000 0.000000 0.3008107 0.1930326 0.2210164
#> ThoughtFuture RespCriticism
#> EmoReactivity 0.1446363 0.0000000
#> TendWorry 0.2991518 0.0000000
#> StressSens 0.0000000 0.0000000
#> SelfAware 0.0000000 0.3008107
#> Moodiness 0.0000000 0.1930326
#> Cautious 0.0000000 0.2210164
#> ThoughtFuture 0.0000000 0.0000000
#> RespCriticism 0.0000000 0.0000000
# Create and view a summary of the network estimation
sum_result_mis <- summary(result_mis)
sum_result_mis
#> The density of the estimated network is 0.321
#>
#> Network was estimated using neighborhood selection on data with missing values.
#> Missing data were handled using 'two-step-em'.
#> The penalty term was log(n) and the 'and' rule was used for edge inclusion.
#>
#> The sample sizes used for the nodewise regressions were as follows:
#> EmoReactivity TendWorry StressSens SelfAware Moodiness
#> 427 426 425 428 424
#> Cautious ThoughtFuture RespCriticism
#> 423 422 420