import numpy as np
import pandas as pd
import statsmodels.api as sm

df = pd.read_csv("dataset.csv")
for v in ["G1", "G2", "studytime"]:
    df[v + "_c"] = df[v] - df[v].mean()

df["M_x_W"] = df["G2_c"] * df["studytime_c"]

covars = ["failures", "absences", "age", "Medu", "Fedu"]
X_m = sm.add_constant(df[["G1_c"] + covars])
model_m = sm.OLS(df["G2"], X_m).fit()

X_y = sm.add_constant(
    df[["G1_c", "G2_c", "studytime_c", "M_x_W"] + covars]
)
model_y = sm.OLS(df["G3"], X_y).fit()

a = model_m.params["G1_c"]
b = model_y.params["G2_c"]
q = model_y.params["M_x_W"]
index = a * q

for w in [-df["studytime"].std(), 0, df["studytime"].std()]:
    print(w, a * (b + q * w))

df <- read.csv("dataset.csv")
df$G1_c <- df$G1 - mean(df$G1)
df$G2_c <- df$G2 - mean(df$G2)
df$studytime_c <- df$studytime - mean(df$studytime)
df$M_x_W <- df$G2_c * df$studytime_c

m_model <- lm(
  G2 ~ G1_c + failures + absences + age + Medu + Fedu,
  data = df
)

y_model <- lm(
  G3 ~ G1_c + G2_c + studytime_c + M_x_W +
    failures + absences + age + Medu + Fedu,
  data = df
)

a <- coef(m_model)["G1_c"]
b <- coef(y_model)["G2_c"]
q <- coef(y_model)["M_x_W"]
index <- a * q

DESCRIPTIVES VARIABLES=G1 G2 studytime /SAVE.
COMPUTE G1_c = G1 - 11.3990755.
COMPUTE G2_c = G2 - 11.5701079.
COMPUTE studytime_c = studytime - 1.9306626.
COMPUTE M_x_W = G2_c * studytime_c.
EXECUTE.

REGRESSION
 /DEPENDENT G2
 /METHOD=ENTER G1_c failures absences age Medu Fedu
 /STATISTICS COEFF OUTS CI(95).

REGRESSION
 /DEPENDENT G3
 /METHOD=ENTER G1_c G2_c studytime_c M_x_W
               failures absences age Medu Fedu
 /STATISTICS COEFF OUTS CI(95) COLLIN
 /SAVE PRED RESID.

Centered G1       = G1 - AVERAGE(G1_range)
Centered G2       = G2 - AVERAGE(G2_range)
Centered W        = studytime - AVERAGE(studytime_range)
Interaction       = Centered_G2 * Centered_W
Conditional b     = b_G2 + b_interaction * Centered_W
Indirect effect   = a_path * Conditional_b
Index             = a_path * b_interaction

In this model, studytime moderates the second-stage M-to-Y path rather than the G1-to-G2 path. A first-stage model would instead include an X-by-W term in the mediator equation. Compare structures before estimation and justify the moderated path theoretically. See main effects versus interaction effects. This Moderated Mediation interpretation should be evaluated with the complete model specification and reported uncertainty.

The index equals the a path multiplied by the interaction coefficient. Its bootstrap interval directly tests whether the indirect effect changes with the moderator. The estimated index is −0.0390, indicating a small decline per one-unit increase in centered studytime. Interpret the interval using the confidence interval guide.

Conditional indirect effects are not separate mediation models. They are evaluations of the same fitted equations at selected moderator values. Low, mean and high studytime produce 0.8156, 0.7832 and 0.7508.

Centering changes the zero point of G1, G2 and studytime, making lower-order coefficients meaningful at the sample mean. Centering does not remove multicollinearity caused by substantive overlap.

The interaction coefficient is the change in the G2 slope for a one-unit increase in centered studytime. Because the coefficient is negative, the mediator-to-outcome slope becomes slightly flatter.

The total effect of G1 on G3 is 0.9339. The direct effect after G2 enters is 0.1473. The difference is represented by the conditional indirect pathway, whose size varies by studytime.

The direct effect remains significant, so the model shows partial mediation rather than complete mediation. Complete mediation should never be declared solely because one p-value crosses .05.

Percentile bootstrap intervals use empirical quantiles of resampled effects. They are especially useful because indirect-effect distributions are often asymmetric and poorly approximated by a normal distribution.

Bias-corrected intervals adjust for median bias and skewness. They may differ from simple percentile intervals, especially with small samples or highly asymmetric effects.

One thousand bootstrap samples provide a usable estimate, but 5,000 or more are commonly preferred for publication when computationally feasible because tail quantiles become more stable.

A Johnson-Neyman analysis can identify moderator regions where the M-to-Y slope or indirect effect is statistically distinguishable from zero. This extends the three-point evaluation used in simple effects analysis.

A categorical moderator requires dummy or effect coding. Conditional indirect effects are then compared across meaningful groups rather than at ±1 SD.

Multiple moderators create additional interaction terms and more complex conditional effects. Theory should determine which path each moderator changes.

Multiple mediators can be modelled in parallel when each transmits a distinct mechanism. Shared variance among mediators must be interpreted carefully.

Serial mediation represents a chain such as G1 → study behaviour → G2 → G3. Temporal and causal ordering must be justified before such a model is interpreted.

Parallel mediation estimates several indirect pathways simultaneously without imposing an order among mediators.

A moderator can also alter the direct X-to-Y effect. That requires an X-by-W term in the outcome equation in addition to any moderated mediator path.

Covariates should be chosen because they address a defined confounding or precision question, not because they happen to be available. Unnecessary controls can change the estimand and reduce interpretability.

Mediation implies a process over time, yet cross-sectional data do not establish temporal precedence. The grade sequence G1, G2 and G3 provides some ordering, but causal claims still require stronger assumptions.

Measurement error in G1, G2 or studytime can attenuate paths and distort interaction estimates. Latent-variable moderated mediation can address measurement models directly.

G1 and G2 are strongly related, so review variance inflation factor and tolerance statistics. A high condition index in SPSS may partly reflect the intercept and centered grade structure.

Use the Breusch-Pagan test and residual plots to evaluate unequal variance. Bootstrap inference protects the indirect effect more than it protects every coefficient estimate.

Large negative residuals from zero-grade cases may influence the outcome equation. Review Cook’s distance and influence diagnostics before deleting any case.

Power depends on the product of the a path and the moderated b-path change. Small interaction effects often require large samples. Plan simulations and consult statistical power rather than relying on a simple events-per-variable rule.

Moderated mediation estimates conditional associations unless treatment assignment, temporal order, no-unmeasured-confounding assumptions and correct model specification support causal interpretation.

Replication should evaluate the index, conditional indirect effects and calibration of the outcome equation in another cohort. Resampling within one dataset cannot establish transportability.