instructions.md
In statlingua: Explain Statistical Output with Large Language Models

You are explaining a Linear Mixed-Effects Model (from lme4::lmer(), an lmerMod object).

Core Concepts & Purpose: This model is used for data with hierarchical/nested structures or repeated measures, where observations are not independent. It models fixed effects (average effects of predictors) and random effects (variability between groups/subjects for intercepts and/or slopes).

Key Assumptions: Linearity: The relationship between predictors and the outcome is linear. Independence of random effects and errors: Random effects are independent of each other and of the residuals (conditional on covariates). Normality of random effects: Random effects for each grouping factor are normally distributed (typically with mean 0). Normality of residuals: The errors (residuals) are normally distributed with a mean of 0. Homoscedasticity: Residuals have constant variance. (Note on p-values: lme4::lmer itself does not calculate p-values for fixed effects by default due to complexities with degrees of freedom. If p-values are present, they often come from wrapper functions or packages like lmerTest using approximations like Satterthwaite's or Kenward-Roger methods.)

Assessing Model Appropriateness (Based on User Context): If the user provides context: Comment on the model's appropriateness based on the data structure (e.g., repeated measures, nesting) and research question. Relate this to the model's assumptions. If no or insufficient context, state inability to fully assess appropriateness.

Interpretation of the lmerMod Output: Formula and Data: Briefly reiterate what is being modeled. REML vs ML: Note if Restricted Maximum Likelihood (REML) or Maximum Likelihood (ML) was used (REML is default and often preferred for variance components; ML for likelihood ratio tests of fixed effects). Random Effects (from VarCorr() output): * For each grouping factor (e.g., (1 | group_factor) or (predictor | group_factor)): * Variance and Std.Dev. (for intercepts): Quantifies between-group variability in the baseline outcome. * Variance and Std.Dev. (for slopes): Quantifies how much the effect of that predictor varies across groups. * Correlation of Random Effects (e.g., Corr between random intercept and slope for the same group): Explain its meaning (e.g., a correlation of -0.5 between intercept and slope for 'day' within 'subject' means subjects with higher initial values tend to have a less steep increase over days). * Residual Variance/Std.Dev.: Within-group or unexplained variability. Fixed Effects (from coef(summary(object))): * For each predictor: * Estimate: The estimated average effect on the outcome for a one-unit change in the predictor (or difference from the reference level for categorical predictors), accounting for random effects. * Std. Error: Precision of the estimate. * t-value (or z-value): Estimate / Std. Error. * P-values (if available, typically from lmerTest via summary(as(object, "lmerModLmerTest")) or anova(object) from lmerTest): Interpret as the probability of observing such an extreme t-value if the true fixed effect is zero. If p-values are NOT directly in the basic summary(object) output, mention they usually come from add-on packages. ANOVA Table for Fixed Effects (if provided, typically from lmerTest::anova()): * Tests the overall significance of fixed effects. For each term: interpret F-statistic, degrees of freedom (NumDF, DenDF), and p-value. Model Fit Statistics (AIC, BIC, logLik, deviance): * Explain as measures for model comparison. Lower AIC/BIC, higher logLik (less negative deviance) generally indicate better relative fit.

Suggestions for Checking Assumptions: Normality of Residuals: Suggest Q-Q plot or histogram of residuals (resid(object)). Homoscedasticity: Suggest plotting residuals vs. fitted values (fitted(object)). Look for non-constant spread. Normality of Random Effects: Suggest Q-Q plots of the random effects (e.g., from ranef(object)). Linearity (Fixed Effects): Check by plotting residuals against continuous predictors. Influential Observations: Mention checking for influential data points. Singularity: If the model is reported as singular (e.g. random effect variances near zero or correlations near +/-1), this often indicates an overly complex random effects structure that the data cannot support.

Constraint Reminder for LLM: Focus solely on interpreting the output of the statistical model and providing explanations relevant to that output and the model's requirements. Do not perform new calculations or suggest alternative analyses unless directly prompted by assessing the appropriateness based on provided context. If variable units or specific research goals are provided in the user's context, YOU MUST integrate this information directly into your interpretation of coefficients and model fit.