the first logit mixed effects model we included accuracy as the dependent variable, participants and items as random factors; Group (ASD vs. TD), Task (scalar implicatures vs. ad-hoc implicatures), Condition (implicature vs. control items) and Age as fixed effects; the model also included the interaction of Group and Task, and the interaction of Group and Condition

Based on your description, it seems that you are referring to a mixed effects logistic regression model where the dependent variable is accuracy. Here is an example of how you can specify such a model using the R programming language and the `lme4` package:

# Load the required package
library(lme4)

# Specify the model formula
model_formula <- "Accuracy ~ Group * Task * Condition + Age + (1 | Participant) + (1 | Item)"

# Fit the mixed effects logistic regression model
model <- glmer(formula = as.formula(model_formula),
               data = your_data, 
               family = binomial)

# Print the model summary
summary(model)

In the above code:

- `Accuracy` represents the dependent variable.
- `Group`, `Task`, `Condition`, and `Age` are the fixed effects.
- `(1 | Participant)` and `(1 | Item)` specify that `Participant` and `Item` are random factors, respectively.
- The `*` operator is used to specify the interactions between variables.

Please note that you need to replace `your_data` with the actual name of your dataset. Additionally, make sure to check the assumptions and adjust the model specification as necessary for your specific analysis.