Jihong Zhang 
This is a quick note illustrate some importance functions of
BGGMand illustrate them using one or more example(s).
GGGMpcor_to_df <- function(x, names = paste0("B", 1:5)) {
colnames(x) = rownames(x) = names
x_upper <- x
x_upper[lower.tri(x_upper)] <- 0
as.data.frame(x_upper) |>
rownames_to_column('Start') |>
pivot_longer(-Start, names_to = 'End', values_to = 'Mean') |>
filter(Mean != 0) |>
mutate(Label = paste0(Start,'-', End))
}A dataset containing items that measure Post-traumatic stress disorder symptoms (Armour et al. 2017). There are 20 variables (p) and 221 observations (n).
The GGM can be estimated using estimate function with some important arguments:
type: could be continuous, binary, ordinal, or mixed
iter: Number of iterations (posterior samples; defaults to 5000).
prior_sd: Scale of the prior distribution, approximately the standard deviation of a beta distribution (defaults to 0.50).
library(BGGM)
library(tidyverse) # for ggplot2 and dplyr
library(psychonetrics) # the frequentist way for GGM
# data
Y <- ptsd[, 1:5] + 1 # add + 1 to make sure the ordinal variable start from '1'
# ordinal model
fit <- estimate(Y, type = 'ordinal', analytic = FALSE)
fit_cont <- estimate(Y, type = 'continuous', analytic = FALSE)
#summary(fit)
pcor_mat(fit) B1 B2 B3 B4 B5
B1 0.000 0.258 0.034 0.353 0.122
B2 0.258 0.000 0.523 -0.084 0.117
B3 0.034 0.523 0.000 0.252 0.203
B4 0.353 -0.084 0.252 0.000 0.359
B5 0.122 0.117 0.203 0.359 0.000Let’s compare the partial correlation estimates to psychonetrics
mod_saturated_ord <- ggm(Y, ordered = TRUE)
mod_saturated_cont <- ggm(Y)
getmatrix(mod_saturated_ord, 'omega') [,1] [,2] [,3] [,4] [,5]
[1,] 0.00000000 0.2655136 0.01768286 0.3593433 0.1242903
[2,] 0.26551363 0.0000000 0.55895807 -0.1174681 0.1195668
[3,] 0.01768286 0.5589581 0.00000000 0.2819463 0.1845554
[4,] 0.35934330 -0.1174681 0.28194629 0.0000000 0.3738825
[5,] 0.12429026 0.1195668 0.18455542 0.3738825 0.0000000freqEst <- pcor_to_df(getmatrix(mod_saturated_ord, 'omega'))
freqEst_cont <- pcor_to_df(getmatrix(mod_saturated_cont, 'omega'))
# transform partial corr. mat. of BGGM into df.
BayesEst <- pcor_to_df(pcor_mat(fit))
BayesEst_cont <- pcor_to_df(pcor_mat(fit_cont))
combEst <- rbind(
freqEst |> mutate(Type = 'psychonetrics_ord'),
BayesEst |> mutate(Type = 'BGGM_ord'),
freqEst_cont |> mutate(Type = 'psychonetrics_cont'),
BayesEst_cont |> mutate(Type = 'BGGM_cont')
) |>
mutate(Type = factor(Type, levels = c("psychonetrics_ord", "BGGM_ord", "psychonetrics_cont","BGGM_cont")))
ggplot(combEst) +
geom_col(aes(x = fct_rev(Label), y = Mean, fill = Type, col = Type), position = position_dodge()) +
geom_text(aes(x = fct_rev(Label), y = ifelse(Mean>0, Mean+.03, Mean-.03), label = round(Mean, 3), group = Type), position = position_dodge(width = .9)) +
labs(x = '') +
coord_flip() +
theme_classic()
We can find that:
psychonetric do not align well with partial correlations with ordinal responses estimated by BGGMpsychonetric align well with partial correlations with continuous responses estimated by BGGMBGGM_cont vs. BGGM_ord)It is easy to conduct regularization using Graph Selection using hypothesis testing
fit_reg <- BGGM::select(fit, alternative = "greater")
plot(fit_reg)$plt
Using BGGM, we can perform hypothesis testing like whether edge A is more strong than edge B, whether edge A is “significant” higher or smaller than 0, whether group A and group B have differences in partial correlations.
# example hypotheses
hyp1 <- c("B2--B3 > B1--B4 > 0") # hypothesis 1
hyp2 <- c("B1--B5 > B2--B5 > 0") # hypothesis 2
hyp3 <- c("B2--B4 < 0") # hypothesis 3
hyp4 <- c("B1--B3 < 0") # hypothesis 4
## Posterior hypothesis probabilities.
extract_php <- function(Y = Y, hypothesis = hyp, type = 'ordinal') {
x <- confirm(Y = Y, hypothesis = hypothesis, type = type)
x_info <- x$info
PHP_confirmatory <- as.matrix(x_info$PHP_confirmatory)
rownames(PHP_confirmatory) <- c(x$hypothesis, "complement")
PHP_confirmatory
}
extract_php(Y = Y, hypothesis = hyp1, type = 'ordinal') [,1]
B2--B3 > B1--B4 > 0 0.982
complement 0.018extract_php(Y = Y, hypothesis = hyp2, type = 'ordinal') [,1]
B1--B5 > B2--B5 > 0 0.855
complement 0.145extract_php(Y = Y, hypothesis = hyp3, type = 'ordinal') [,1]
B2--B4 < 0 0.686
complement 0.314extract_php(Y = Y, hypothesis = hyp4, type = 'ordinal') [,1]
B1--B3 < 0 0.272
complement 0.728There are four hypothesis tested here:
B2--B3 is larger than B1--B4 . In other words, that the partial correlation is larger for B2--B3. The p(H1|data) = 0.991 means the posterior hypothesis probability (PHP) is 0.991 which provides evidence for the hypothesis: the partial correlation for B2-B3 is larger;B1--B5 is larger than B2--B5 . The results of PHP suggests the hypothesis can be accepted;B2--B4 is larger than 0 . The results of PHP suggests the hypothesis can be accepted;B1--B3 is lower than 0 . The results of PHP suggests the hypothesis should be rejected given p(H_1) < p(complement);# data
Y <- bfi
# males
Ymales <- subset(Y, gender == 1,
select = -c(gender, education))
# females
Yfemales <- subset(Y, gender == 2,
select = -c(gender, education))
# model fit
fit <- ggm_compare_estimate(Ymales, Yfemales)
# plot summary
summary(fit)BGGM: Bayesian Gaussian Graphical Models
---
Type: continuous
Analytic: FALSE
Formula:
Posterior Samples: 5000
Observations (n):
Group 1: 805
Group 2: 1631
Nodes (p): 25
Relations: 300
---
Call:
ggm_compare_estimate(Ymales, Yfemales)
---
Estimates:
Relation Post.mean Post.sd Cred.lb Cred.ub
A1--A2 0.048 0.039 -0.029 0.125
A1--A3 -0.022 0.040 -0.101 0.054
A2--A3 -0.033 0.038 -0.111 0.044
A1--A4 -0.006 0.041 -0.088 0.075
A2--A4 -0.049 0.040 -0.128 0.028
A3--A4 0.038 0.039 -0.039 0.114
A1--A5 0.000 0.041 -0.082 0.081
A2--A5 0.086 0.041 0.004 0.165
A3--A5 0.063 0.038 -0.011 0.138
A4--A5 -0.024 0.040 -0.102 0.057
A1--C1 -0.020 0.041 -0.101 0.058
A2--C1 -0.027 0.041 -0.110 0.052
A3--C1 0.025 0.041 -0.054 0.106
A4--C1 0.010 0.041 -0.070 0.091
A5--C1 0.051 0.041 -0.029 0.133
A1--C2 -0.025 0.041 -0.105 0.054
A2--C2 0.013 0.041 -0.068 0.094
A3--C2 0.003 0.041 -0.074 0.082
A4--C2 0.046 0.040 -0.036 0.125
A5--C2 0.014 0.041 -0.063 0.094
C1--C2 0.024 0.038 -0.049 0.100
A1--C3 0.012 0.040 -0.066 0.091
A2--C3 0.022 0.040 -0.057 0.100
A3--C3 -0.032 0.042 -0.113 0.051
A4--C3 0.034 0.041 -0.046 0.113
A5--C3 -0.019 0.041 -0.101 0.062
C1--C3 0.041 0.040 -0.036 0.119
C2--C3 0.023 0.040 -0.055 0.101
A1--C4 0.015 0.040 -0.061 0.095
A2--C4 0.021 0.041 -0.059 0.101
A3--C4 0.103 0.040 0.024 0.184
A4--C4 -0.038 0.041 -0.119 0.043
A5--C4 -0.047 0.040 -0.125 0.031
C1--C4 0.062 0.041 -0.017 0.142
C2--C4 0.029 0.038 -0.045 0.102
C3--C4 0.003 0.040 -0.075 0.083
A1--C5 -0.039 0.041 -0.118 0.042
A2--C5 -0.005 0.041 -0.085 0.075
A3--C5 0.034 0.041 -0.047 0.114
A4--C5 0.048 0.040 -0.032 0.125
A5--C5 0.048 0.041 -0.032 0.128
C1--C5 -0.084 0.041 -0.164 -0.005
C2--C5 0.074 0.041 -0.008 0.155
C3--C5 0.098 0.040 0.018 0.174
C4--C5 0.050 0.038 -0.024 0.123
A1--E1 0.051 0.041 -0.030 0.129
A2--E1 0.017 0.041 -0.064 0.097
A3--E1 0.024 0.041 -0.057 0.102
A4--E1 0.001 0.041 -0.078 0.082
A5--E1 0.006 0.041 -0.073 0.086
C1--E1 0.062 0.041 -0.019 0.143
C2--E1 0.005 0.040 -0.075 0.084
C3--E1 0.068 0.040 -0.012 0.147
C4--E1 -0.007 0.041 -0.087 0.074
C5--E1 0.010 0.040 -0.071 0.090
A1--E2 0.009 0.041 -0.069 0.089
A2--E2 0.041 0.041 -0.040 0.121
A3--E2 -0.011 0.041 -0.091 0.066
A4--E2 -0.051 0.040 -0.130 0.027
A5--E2 -0.027 0.041 -0.106 0.053
C1--E2 -0.002 0.041 -0.083 0.079
C2--E2 0.039 0.041 -0.042 0.119
C3--E2 -0.159 0.040 -0.238 -0.078
C4--E2 -0.018 0.041 -0.101 0.063
C5--E2 0.081 0.040 0.003 0.159
E1--E2 0.012 0.039 -0.064 0.088
A1--E3 -0.033 0.041 -0.115 0.045
A2--E3 -0.067 0.041 -0.148 0.015
A3--E3 -0.037 0.040 -0.115 0.043
A4--E3 -0.005 0.040 -0.082 0.074
A5--E3 -0.034 0.041 -0.114 0.046
C1--E3 0.069 0.041 -0.011 0.149
C2--E3 -0.001 0.040 -0.079 0.078
C3--E3 -0.034 0.041 -0.114 0.045
C4--E3 -0.007 0.041 -0.088 0.071
C5--E3 0.000 0.040 -0.080 0.078
E1--E3 -0.032 0.041 -0.109 0.049
E2--E3 -0.063 0.041 -0.147 0.014
A1--E4 0.033 0.041 -0.046 0.115
A2--E4 0.031 0.042 -0.051 0.112
A3--E4 0.026 0.040 -0.054 0.105
A4--E4 -0.063 0.040 -0.143 0.017
A5--E4 -0.025 0.039 -0.103 0.052
C1--E4 -0.004 0.041 -0.084 0.077
C2--E4 -0.077 0.041 -0.159 0.002
C3--E4 0.023 0.041 -0.057 0.104
C4--E4 -0.026 0.041 -0.106 0.052
C5--E4 -0.022 0.041 -0.101 0.057
E1--E4 -0.036 0.039 -0.114 0.040
E2--E4 0.031 0.039 -0.047 0.107
E3--E4 0.029 0.041 -0.051 0.110
A1--E5 -0.013 0.041 -0.093 0.065
A2--E5 0.022 0.040 -0.057 0.101
A3--E5 -0.023 0.040 -0.098 0.056
A4--E5 0.121 0.041 0.040 0.200
A5--E5 -0.023 0.041 -0.104 0.059
C1--E5 -0.018 0.041 -0.099 0.063
C2--E5 0.005 0.041 -0.073 0.084
C3--E5 -0.028 0.041 -0.107 0.051
C4--E5 0.007 0.041 -0.074 0.089
C5--E5 -0.024 0.041 -0.102 0.058
E1--E5 0.004 0.041 -0.077 0.084
E2--E5 0.000 0.041 -0.080 0.080
E3--E5 0.063 0.040 -0.015 0.139
E4--E5 0.090 0.040 0.011 0.172
A1--N1 0.059 0.040 -0.019 0.138
A2--N1 0.060 0.041 -0.021 0.141
A3--N1 -0.048 0.041 -0.130 0.032
A4--N1 0.025 0.041 -0.057 0.105
A5--N1 -0.004 0.041 -0.084 0.078
C1--N1 -0.039 0.041 -0.119 0.043
C2--N1 -0.001 0.041 -0.081 0.076
C3--N1 0.069 0.041 -0.013 0.150
C4--N1 -0.037 0.041 -0.118 0.041
C5--N1 -0.021 0.041 -0.105 0.059
E1--N1 0.068 0.041 -0.015 0.148
E2--N1 -0.022 0.042 -0.102 0.061
E3--N1 -0.010 0.042 -0.091 0.070
E4--N1 -0.008 0.041 -0.087 0.074
E5--N1 -0.018 0.041 -0.099 0.062
A1--N2 -0.041 0.040 -0.119 0.037
A2--N2 -0.121 0.041 -0.198 -0.041
A3--N2 0.074 0.041 -0.007 0.154
A4--N2 -0.049 0.040 -0.127 0.032
A5--N2 0.061 0.042 -0.021 0.143
C1--N2 0.042 0.040 -0.038 0.121
C2--N2 -0.051 0.041 -0.129 0.029
C3--N2 -0.030 0.041 -0.110 0.050
C4--N2 -0.028 0.041 -0.108 0.053
C5--N2 0.037 0.041 -0.042 0.119
E1--N2 0.006 0.041 -0.074 0.087
E2--N2 -0.034 0.041 -0.114 0.046
E3--N2 -0.048 0.041 -0.131 0.031
E4--N2 0.043 0.042 -0.039 0.124
E5--N2 0.044 0.041 -0.035 0.126
N1--N2 0.049 0.028 -0.008 0.103
A1--N3 -0.072 0.040 -0.152 0.005
A2--N3 0.060 0.042 -0.023 0.141
A3--N3 -0.031 0.041 -0.113 0.048
A4--N3 0.024 0.041 -0.056 0.103
A5--N3 0.051 0.041 -0.031 0.130
C1--N3 0.036 0.041 -0.046 0.116
C2--N3 -0.007 0.040 -0.084 0.073
C3--N3 0.043 0.041 -0.038 0.123
C4--N3 0.074 0.041 -0.008 0.153
C5--N3 0.042 0.041 -0.037 0.124
E1--N3 -0.082 0.041 -0.162 -0.001
E2--N3 -0.032 0.040 -0.110 0.047
E3--N3 -0.081 0.041 -0.161 0.001
E4--N3 -0.117 0.041 -0.197 -0.034
E5--N3 0.045 0.041 -0.034 0.126
N1--N3 -0.005 0.039 -0.082 0.068
N2--N3 -0.100 0.040 -0.177 -0.021
A1--N4 0.054 0.041 -0.027 0.135
A2--N4 0.018 0.041 -0.062 0.098
A3--N4 0.039 0.041 -0.041 0.122
A4--N4 0.025 0.042 -0.059 0.106
A5--N4 -0.096 0.041 -0.174 -0.013
C1--N4 0.054 0.041 -0.025 0.131
C2--N4 -0.033 0.041 -0.115 0.048
C3--N4 -0.086 0.041 -0.167 -0.006
C4--N4 -0.102 0.041 -0.181 -0.023
C5--N4 0.034 0.040 -0.046 0.112
E1--N4 0.007 0.040 -0.073 0.085
E2--N4 -0.016 0.041 -0.098 0.062
E3--N4 0.156 0.041 0.075 0.236
E4--N4 0.091 0.041 0.012 0.170
E5--N4 -0.090 0.041 -0.169 -0.010
N1--N4 -0.067 0.041 -0.149 0.012
N2--N4 0.066 0.041 -0.014 0.146
N3--N4 0.086 0.037 0.014 0.157
A1--N5 -0.065 0.040 -0.143 0.012
A2--N5 -0.034 0.042 -0.115 0.049
A3--N5 -0.010 0.041 -0.092 0.070
A4--N5 -0.041 0.041 -0.120 0.039
A5--N5 -0.031 0.041 -0.112 0.049
C1--N5 -0.016 0.041 -0.097 0.063
C2--N5 -0.024 0.041 -0.103 0.054
C3--N5 0.045 0.041 -0.035 0.125
C4--N5 0.070 0.040 -0.008 0.150
C5--N5 -0.106 0.041 -0.185 -0.025
E1--N5 -0.016 0.041 -0.097 0.066
E2--N5 0.032 0.040 -0.045 0.109
E3--N5 0.002 0.041 -0.081 0.081
E4--N5 -0.017 0.040 -0.095 0.063
E5--N5 0.032 0.040 -0.045 0.110
N1--N5 -0.054 0.041 -0.136 0.027
N2--N5 0.013 0.041 -0.067 0.094
N3--N5 -0.013 0.040 -0.092 0.066
N4--N5 0.028 0.040 -0.048 0.108
A1--O1 -0.022 0.040 -0.102 0.058
A2--O1 -0.008 0.041 -0.088 0.072
A3--O1 0.043 0.040 -0.036 0.123
A4--O1 0.019 0.041 -0.061 0.099
A5--O1 -0.086 0.040 -0.165 -0.009
C1--O1 -0.008 0.041 -0.089 0.073
C2--O1 0.045 0.040 -0.033 0.123
C3--O1 -0.096 0.041 -0.176 -0.016
C4--O1 0.001 0.042 -0.081 0.084
C5--O1 -0.040 0.041 -0.121 0.041
E1--O1 -0.053 0.040 -0.130 0.025
E2--O1 0.054 0.041 -0.028 0.135
E3--O1 -0.063 0.040 -0.143 0.016
E4--O1 0.004 0.040 -0.075 0.083
E5--O1 -0.041 0.040 -0.120 0.039
N1--O1 -0.034 0.041 -0.114 0.049
N2--O1 -0.007 0.041 -0.087 0.074
N3--O1 0.065 0.041 -0.014 0.143
N4--O1 -0.002 0.041 -0.085 0.078
N5--O1 -0.021 0.041 -0.104 0.059
A1--O2 0.002 0.040 -0.076 0.080
A2--O2 0.036 0.041 -0.042 0.116
A3--O2 0.048 0.041 -0.032 0.126
A4--O2 0.021 0.040 -0.058 0.100
A5--O2 -0.039 0.041 -0.119 0.040
C1--O2 -0.014 0.040 -0.096 0.064
C2--O2 -0.064 0.041 -0.144 0.015
C3--O2 -0.015 0.042 -0.098 0.063
C4--O2 -0.008 0.040 -0.087 0.073
C5--O2 -0.072 0.041 -0.153 0.007
E1--O2 0.072 0.041 -0.010 0.153
E2--O2 0.093 0.041 0.014 0.173
E3--O2 0.024 0.041 -0.057 0.103
E4--O2 0.021 0.040 -0.058 0.099
E5--O2 0.038 0.041 -0.041 0.119
N1--O2 -0.013 0.041 -0.095 0.065
N2--O2 -0.005 0.041 -0.086 0.075
N3--O2 0.034 0.040 -0.044 0.112
N4--O2 -0.030 0.041 -0.109 0.050
N5--O2 0.011 0.041 -0.070 0.092
O1--O2 0.049 0.040 -0.031 0.127
A1--O3 0.042 0.041 -0.041 0.120
A2--O3 0.044 0.041 -0.038 0.126
A3--O3 0.032 0.041 -0.048 0.111
A4--O3 0.003 0.041 -0.077 0.084
A5--O3 0.005 0.041 -0.076 0.084
C1--O3 -0.035 0.041 -0.116 0.046
C2--O3 0.036 0.040 -0.043 0.114
C3--O3 0.012 0.041 -0.068 0.091
C4--O3 -0.056 0.041 -0.137 0.023
C5--O3 0.034 0.041 -0.046 0.114
E1--O3 0.004 0.041 -0.076 0.084
E2--O3 0.081 0.041 -0.003 0.161
E3--O3 0.020 0.040 -0.059 0.097
E4--O3 -0.022 0.041 -0.101 0.056
E5--O3 -0.100 0.041 -0.180 -0.021
N1--O3 0.051 0.041 -0.028 0.131
N2--O3 -0.027 0.042 -0.108 0.054
N3--O3 -0.018 0.040 -0.096 0.062
N4--O3 -0.040 0.041 -0.121 0.041
N5--O3 0.038 0.041 -0.045 0.118
O1--O3 0.066 0.039 -0.012 0.144
O2--O3 0.015 0.040 -0.063 0.095
A1--O4 0.121 0.041 0.040 0.199
A2--O4 0.010 0.041 -0.070 0.092
A3--O4 0.041 0.040 -0.038 0.120
A4--O4 0.049 0.041 -0.033 0.128
A5--O4 -0.024 0.041 -0.104 0.056
C1--O4 -0.021 0.041 -0.101 0.060
C2--O4 -0.032 0.041 -0.111 0.049
C3--O4 -0.031 0.042 -0.115 0.049
C4--O4 0.012 0.040 -0.066 0.089
C5--O4 0.028 0.040 -0.050 0.107
E1--O4 0.064 0.041 -0.015 0.142
E2--O4 0.024 0.041 -0.056 0.105
E3--O4 0.055 0.041 -0.028 0.133
E4--O4 0.002 0.040 -0.075 0.081
E5--O4 0.011 0.040 -0.070 0.090
N1--O4 -0.018 0.041 -0.097 0.063
N2--O4 0.018 0.041 -0.062 0.098
N3--O4 -0.062 0.041 -0.140 0.016
N4--O4 -0.006 0.040 -0.086 0.072
N5--O4 -0.016 0.040 -0.097 0.063
O1--O4 0.071 0.040 -0.008 0.151
O2--O4 -0.043 0.041 -0.123 0.037
O3--O4 -0.027 0.040 -0.105 0.052
A1--O5 0.059 0.041 -0.024 0.136
A2--O5 -0.015 0.041 -0.095 0.064
A3--O5 -0.003 0.041 -0.085 0.076
A4--O5 0.040 0.040 -0.038 0.118
A5--O5 0.069 0.041 -0.009 0.151
C1--O5 -0.061 0.041 -0.141 0.019
C2--O5 0.041 0.041 -0.038 0.124
C3--O5 -0.016 0.041 -0.094 0.065
C4--O5 0.006 0.040 -0.073 0.084
C5--O5 0.093 0.040 0.012 0.172
E1--O5 0.018 0.040 -0.061 0.097
E2--O5 0.013 0.041 -0.067 0.093
E3--O5 0.020 0.041 -0.060 0.100
E4--O5 0.063 0.040 -0.016 0.141
E5--O5 -0.063 0.040 -0.141 0.015
N1--O5 0.023 0.040 -0.057 0.100
N2--O5 -0.039 0.041 -0.119 0.040
N3--O5 0.083 0.041 0.005 0.165
N4--O5 -0.025 0.041 -0.106 0.054
N5--O5 0.009 0.041 -0.071 0.089
O1--O5 -0.024 0.041 -0.104 0.059
O2--O5 -0.026 0.039 -0.105 0.049
O3--O5 -0.008 0.039 -0.084 0.070
O4--O5 0.043 0.040 -0.035 0.123
--- The regularized group difference network plot can be visualized as:
plot(BGGM::select(fit))[[1]]