vlt.stats.get_lme_effect_sizes

  GET_LME_EFFECT_SIZES Computes effect sizes for a Linear Mixed Effects model.

    effectSizes = GET_LME_EFFECT_SIZES(lme) takes a fitted LinearMixedModel 
    object and returns a structure containing the raw Beta, Cohen's d 
    approximation, Standardized Beta, and N (number of observations) for
    each fixed effect term.

    ERROR CONDITION:
    This function checks for interaction terms (e.g., 'A:B'). If any are 
    present, it throws an error as requested, because simple main effect 
    calculations are misleading in the presence of interactions.

    METHODS / FORMULAS:
    1. Cohen's d Approximation:
       Measures the shift in the response variable relative to the raw 
       standard deviation of the data.

       Formula:  d = Beta / sigma_y

       Where:
         Beta    = The estimated fixed effect coefficient (Raw Estimate).
         sigma_y = The standard deviation of the response variable (y).

    2. Standardized Beta (Beta_std):
       Measures the change in the outcome (in standard deviations) for a 
       1 standard deviation change in the predictor.

       Formula:  Beta_std = Beta * (sigma_x / sigma_y)

       Where:
         sigma_x = The standard deviation of the specific column in the 
                   fixed effects design matrix corresponding to that term. 
                   (For categorical variables, this is the SD of the 0/1 
                   dummy vector).

    3. N (Number of Observations):
       For binary/dummy terms (including Intercept), this is the count of
       observations where the term is 1.
       For continuous variables (or non-binary columns), this is the total
       number of observations used in the model.

    INPUT:
        lme - A fitted LinearMixedModel object (from fitlme).

    OUTPUT:
        effectSizes - A structure containing vectors for:
            .TermNames   (Cell array of coefficient names)
            .RawBeta     (The original estimates)
            .CohensD     (The approximated Cohen's d)
            .StdBeta     (The standardized coefficients)
            .N           (The number of observations per level/term)

    Example:
        lme = fitlme(tbl, 'ReactionTime ~ Drug + (1|Subject)');
        es = get_lme_effect_sizes(lme);