How to obtain Bayes factor for difference between two correlations?

> summary(model) Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod'] Family: binomial ( logit ) Formula: Infestate ~ Trattamento + (1 | ID_pianta) + (1 | Blocco) Data: data AIC BIC logLik deviance df.resid 3835.8 3871.7 -1911.9 3823.8 2931 Scaled residuals: Min 1Q Median 3Q Max -2.1969 -1.0611 0.6139 0.8091 1.5079 Random effects: Groups Name Variance Std.Dev. ID_pianta (Intercept) 0.16880 0.4108 Blocco (Intercept) 0.09686 0.3112 Number of obs: 2937, groups: ID_pianta, 40; Blocco, 3 Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.59808 0.20650 2.896 0.003776 ** TrattamentoLavanda -0.16521 0.11116 -1.486 0.137218 TrattamentoRosmarino -0.02389 0.11000 -0.217 0.828075 TrattamentoTimo -0.37733 0.11017 -3.425 0.000615 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation of Fixed Effects: (Intr) TrttmL TrttmR TrttmntLvnd -0.266 TrttmntRsmr -0.269 0.502 TrattamntTm -0.269 0.499 0.504

I wanted also to check the predictive abilities. I used this code

library(caret) data$Infestate <- factor(data$Infestate, levels = c(0, 1)) # Convert predicted probabilities to binary predictions using a threshold binary_predictions <- ifelse(predicted_probabilities > 0.5, 1, 0) # Convert binary_predictions to a factor with levels 0 and 1 binary_predictions <- factor(binary_predictions, levels = c(0, 1)) # Create a confusion matrix conf_matrix <- confusionMatrix(data$Infestate, binary_predictions) print(conf_matrix)

And these are the results:

Confusion Matrix and Statistics Reference Prediction 0 1 0 1811 28 1 751 55 Accuracy : 0.7055 95% CI : (0.6877, 0.7228) No Information Rate : 0.9686 P-Value [Acc > NIR] : 1 Kappa : 0.0709 Mcnemar's Test P-Value : <2e-16 Sensitivity : 0.70687 Specificity : 0.66265 Pos Pred Value : 0.98477 Neg Pred Value : 0.06824 Prevalence : 0.96862 Detection Rate : 0.68469 Detection Prevalence : 0.69527 Balanced Accuracy : 0.68476 'Positive' Class : 0

It seems te model is good in predicting negative but it predicts 751 false positive. How to deal this aspect? Can the model be considered a good predictor? How can I increase predictive abilities?

However, I don't have access to SPSS so am wondering if anyone has any suggestions on how to do this analysis in r (or even Graphpad Prism).

Or I could the diffcorr package to calculate differences for each combination of groups, but then would I need to apply a multiple comparison correction?

Alternatively, Mohr & Marcon 2005 describe a different method using spearman correlation that seems like it might be more relevant, however I wonder why their method doesn’t seem to have been used by other researches? It also looks difficult to implement so I’m unsure if it’s the right choice.

Any advice would be much appreciated!