knitr::opts_chunk$set(echo = TRUE)

This is a follow-up to the vignette "Three Ways to Test the Same Hypothesis". A
new feature, `pcor_sum`

, was added to **BGGM** that allows for testing partial correlation sums.
This differs from the Bayes factor approach ("Approach #3"), in that only the posterior
distribution is used to determine whether there is a difference in the sums.

# need the developmental version if (!requireNamespace("remotes")) { install.packages("remotes") } # install from github remotes::install_github("donaldRwilliams/BGGM") library(BGGM)

This first example looks at one group, where a sum is tested within the same ptsd network. I focus on the
relations between the re-experiencing (`B`

) and avoidance (`C`

) communities. In particular, the sum of relations between the "Intrusion" (5 nodes) community and the "Avoidance" (two nodes) community is tested.

For the avoidance symptom "avoidance of thoughts" `C1`

, this can be written in `R`

code with

# ptsd Y <- ptsd # paste together sums paste0(colnames(Y)[1:5], "--C1", collapse = " + ") #> "B1--C1 + B2--C1 + B3--C1 + B4--C1 + B5--C1"

whereas, for the avoidance symptom "avoidance of reminders" (`C2`

), this is written as

paste0(colnames(Y)[1:5], "--C2", collapse = " + ") #> "B1--C2 + B2--C2 + B3--C2 + B4--C2 + B5--C2"

Note that typically this would have to be written out. `paste0`

was used in this case to
avoid typing out all of the relations.

Here an ordinal GGM is fitted

fit <- estimate(Y+1, type = "ordinal", iter = 1000)

where the `+1`

changes the first category from 0 to 1 (required).

The next step is to use the `pcor_sum`

function. First, I combine the sums into one string separated with `;`

.

# sum 1 sum1 <- paste0(colnames(Y)[1:5], "--C1", collapse = " + ") # sum 2 sum2 <- paste0(colnames(Y)[1:5], "--C2", collapse = " + ") # paste together sums <- paste(sum1, sum2, sep = ";") # print sums #> "B1--C1 + B2--C1 + B3--C1 + B4--C1 + B5--C1;B1--C2 + B2--C2 + B3--C2 + B4--C2 + B5--C2"

Next `pcor_sum`

is used

test_sum <- pcor_sum(fit, relations = sums) # print test_sum # BGGM: Bayesian Gaussian Graphical Models # --- # Network Stats: Posterior Sum # Posterior Samples: 1000 # --- # Estimates # # Sum: # Post.mean Post.sd Cred.lb Cred.ub # B1--C1+B2--C1+B3--C1+B4--C1+B5--C1 0.215 0.096 0.034 0.404 # B1--C2+B2--C2+B3--C2+B4--C2+B5--C2 0.334 0.097 0.145 0.514 # --- # # Difference: # B1--C1+B2--C1+B3--C1+B4--C1+B5--C1 - B1--C2+B2--C2+B3--C2+B4--C2+B5--C2 # # Post.mean Post.sd Cred.lb Cred.ub Prob.greater Prob.less # -0.119 0.145 -0.409 0.173 0.205 0.795 # ---

`Prob.greater`

is the posterior probability that the first sum is larger than the second sum.

The object `test_sum`

can then be plotted. Note this returns three plots, but only the difference is shown here

plot(test_sum)$diff

The histogram is not very smooth in this case because `iter = 1000`

, but this of course can be changed.

This next example is for two groups. The data are called `bfi`

and they are in the **BGGM** package. I compare a sum of two relations for questions measuring agreeableness in males and females. The relations tested are as follows

sums <- c("A3--A4 + A4--A5")

where `A1`

is "know how to comfort others", `A4`

is "love children", and `A5`

is "make people feel at ease".

The next step is to fit the models

# data Y <- bfi # males Y_males <- subset(Y, gender == 1, select = -c(education, gender))[,1:5] # females Y_females <- subset(Y, gender == 2, select = -c(education, gender))[,1:5] fit_female <- estimate(Y_females, seed = 2) # fit males fit_male <- estimate(Y_males, seed = 1)

Then test the sum

test_sum <- pcor_sum(fit_female, fit_male, relations = sums) # print test_sum #> BGGM: Bayesian Gaussian Graphical Models #> --- #> Network Stats: Posterior Sum #> Posterior Samples: 5000 #> --- #> Estimates #> #> Sum: #> Post.mean Post.sd Cred.lb Cred.ub #> g1: A3--A4+A4--A5 0.292 0.026 0.241 0.342 #> g2: A3--A4+A4--A5 0.305 0.036 0.234 0.375 #> --- #> #> Difference: #> g1: A3--A4+A4--A5 - g2: A3--A4+A4--A5 #> #> Post.mean Post.sd Cred.lb Cred.ub Prob.greater Prob.less #> -0.014 0.045 -0.1 0.074 0.386 0.614 #> ---

For a kind of sanity check, here is the sum for the male group obtained from the point estimates.

pcor_mat(fit_male)["A3", "A4"] + pcor_mat(fit_male)["A4", "A5"] #> 0.305

This matches the output.

By default, the print function for `pcor_sum`

provides 95 % credible intervals. This can be changed by
directly using the print function, for example `print(test_sum, cred = 0.99)`

, provides
99 % credible intervals.

Currently, this function only supports sums, due to this being of interest for the psychological network literature in particular. This can be extended to accommodate multiplication, subtraction, testing values other than zero, etc. Please make a feature request at either github or BGGM-users group.

**Any scripts or data that you put into this service are public.**

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