Introduction
This vignette describes how to control for variables. This is a new
feature to BGGM (version 2.0.0).
Example 1: Multivariate Regression
When controlling for variables, a multivariate regression is fitted in BGGM. In fact, a GGM can be understood as a multivariate regression with intercepts only models for the predictors.
Notes about Implementation
BGGM does not use the typical approach for
multivariate regression in R. This avoids having to write
out each outcome variable, of which there are typically many in a GGM.
In BGGM, it is assumed that the data matrix includes
only the variables to be included in the GGM and the control
variables.
Correct
Suppose that we want to control for education level, with five variables included in the GGM.
# data
Y <- bfi[,c(1:5, 27)]
# head
head(Y)
#> A1 A2 A3 A4 A5 education
#> 61617 2 4 3 4 4 NA
#> 61618 2 4 5 2 5 NA
#> 61620 5 4 5 4 4 NA
#> 61621 4 4 6 5 5 NA
#> 61622 2 3 3 4 5 NA
#> 61623 6 6 5 6 5 3Notice that Y includes only the five
variables and education.
Fit Model
This model can then be fitted with
fit <- explore(Y, formula = ~ as.factor(education))To show this is indeed a multivariate regression, here are the summarized regression coefficients for the first outcome.
summ_coef <- regression_summary(fit)
# outcome one
summ_coef$reg_summary[[1]]
#> Post.mean Post.sd Cred.lb Cred.ub
#> (Intercept) 0.256 0.095 0.072 0.442
#> as.factor(education)2 0.073 0.128 -0.177 0.323
#> as.factor(education)3 -0.202 0.104 -0.405 -0.001
#> as.factor(education)4 -0.462 0.119 -0.691 -0.233
#> as.factor(education)5 -0.578 0.117 -0.815 -0.346And here are the coefficients from lm (a univariate
regression for A1)
round(
cbind(
# summary: coef and se
summary( lm(scale(A1, scale = F) ~ as.factor(education), data = Y))$coefficients[,1:2],
# confidence interval
confint( lm(scale(A1, scale = F) ~ as.factor(education), data = Y))
), 3)
#> Estimate Std. Error 2.5 % 97.5 %
#> (Intercept) 0.256 0.093 0.073 0.438
#> as.factor(education)2 0.072 0.125 -0.172 0.316
#> as.factor(education)3 -0.203 0.101 -0.401 -0.004
#> as.factor(education)4 -0.461 0.116 -0.690 -0.233
#> as.factor(education)5 -0.578 0.115 -0.804 -0.351The estimate are very (very) similar.
Summary
Note that all the other functions work just the same. For example, the relations controlling for education are summarized with
summary(fit)
#> BGGM: Bayesian Gaussian Graphical Models
#> ---
#> Type: continuous
#> Analytic: FALSE
#> Formula: ~ as.factor(education)
#> Posterior Samples: 5000
#> Observations (n):
#> Nodes (p): 5
#> Relations: 10
#> ---
#> Call:
#> estimate(Y = Y, formula = ~as.factor(education))
#> ---
#> Estimates:
#> Relation Post.mean Post.sd Cred.lb Cred.ub
#> A1--A2 -0.239 0.020 -0.278 -0.200
#> A1--A3 -0.109 0.020 -0.150 -0.070
#> A2--A3 0.276 0.019 0.239 0.312
#> A1--A4 -0.013 0.021 -0.055 0.026
#> A2--A4 0.156 0.020 0.117 0.196
#> A3--A4 0.173 0.020 0.134 0.214
#> A1--A5 -0.010 0.020 -0.050 0.029
#> A2--A5 0.150 0.020 0.111 0.189
#> A3--A5 0.358 0.018 0.322 0.392
#> A4--A5 0.121 0.020 0.082 0.159
#> --- Incorrect
Now if we wanted to control for education, but also had gender in
Y, this would be incorrect
Y <- bfi[,c(1:5, 26:27)]
head(Y)
#> A1 A2 A3 A4 A5 gender education
#> 61617 2 4 3 4 4 1 NA
#> 61618 2 4 5 2 5 2 NA
#> 61620 5 4 5 4 4 2 NA
#> 61621 4 4 6 5 5 2 NA
#> 61622 2 3 3 4 5 1 NA
#> 61623 6 6 5 6 5 2 3In this case, with
estimate(Y, formula = as.factor(education)), the GGM would
also include gender (six variables instead of the desired
5). This is because all variables not included in formula
are included in the GGM. This was adopted in BGGM to
save the user from having to write out each outcome.
This differs from lm, where each outcome needs to be
written out, for example
cbind(A1, A2, A3, A4, A4) ~ as.factor(education). This is
quite cumbersome for a model that includes many nodes.
Example 2: Multivariate Probit
The above data is ordinal. In this case, it is possible to fit a multivariate probit model. This is also the approach for binary data in BGGM. This is implemented with
fit <- estimate(Y, formula = ~ as.factor(education),
type = "ordinal", iter = 1000)Note that the multivariate probit models can also be summarized with
regression_summary.
Example 3: Gaussian Copula Graphical Model
This final example fits a Gaussian copula graphical model that can be
used for mixed data. In this case, formula is not used and
instead all of the variables are included in the GGM.
Fit Model
This model is estimated with
# data
Y <- na.omit(bfi[,c(1:5, 27)])
# fit type = "mixed"
fit <- estimate(Y, type = "mixed", iter = 1000)
# summary
summary(fit)
#> BGGM: Bayesian Gaussian Graphical Models
#> ---
#> Type: mixed
#> Analytic: FALSE
#> Formula:
#> Posterior Samples: 1000
#> Observations (n):
#> Nodes (p): 6
#> Relations: 15
#> ---
#> Call:
#> estimate(Y = Y, type = "mixed", iter = 1000)
#> ---
#> Estimates:
#> Relation Post.mean Post.sd Cred.lb Cred.ub
#> A1--A2 -0.217 0.048 -0.294 -0.114
#> A1--A3 -0.063 0.027 -0.113 -0.011
#> A2--A3 0.364 0.023 0.317 0.410
#> A1--A4 0.116 0.038 0.048 0.192
#> A2--A4 0.241 0.031 0.182 0.303
#> A3--A4 0.228 0.026 0.174 0.275
#> A1--A5 0.057 0.031 0.003 0.120
#> A2--A5 0.186 0.027 0.135 0.241
#> A3--A5 0.438 0.019 0.399 0.474
#> A4--A5 0.151 0.025 0.103 0.199
#> A1--education -0.016 0.069 -0.125 0.119
#> A2--education 0.063 0.049 -0.016 0.162
#> A3--education 0.049 0.025 0.002 0.099
#> A4--education 0.053 0.026 0.005 0.105
#> A5--education 0.072 0.024 0.024 0.120
#> --- Here it is clear that education is included in the model, as the relations with the other nodes are included in the output.