GAM (Generalized Additive Models)
GAM (Generalized Additive Models) is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Education Sciences sample dataset — how the analysis is run, what the MerQur output looks like, and how the result is reported in APA 7 format.
🎯 What is it for?
GAM (Generalized Additive Models) automatically performs all required assumption checks (normality, homogeneity of variance, etc.) for the relevant data type in the background and presents the results with a clear table + chart. Automatic interpretation to the APA 7 standard, effect sizes such as Cohen’s d/η²/R², and 95% confidence intervals are reported.
📌 When is it used?
- Statistical analysis of measurements in the Education Sciences domain
- To produce APA 7-compatible result tables for academic publications
- Hypothesis testing and decision-making processes
- Undergraduate / master’s / PhD theses after the appropriate method has been selected
📐 Assumptions
- Appropriate scale — Variables must be at the measurement level required by the analysis (nominal/ordinal/interval/ratio)
- Independent observations — Observations must come from individuals independent of one another
- Sufficient sample size — The minimum n requirement for the analysis must be met
- Outlier check — Outliers must be detected and evaluated
If assumptions are violated, MerQur automatically suggests a non-parametric or robust alternative.
🛠 How to do it in MerQur
Load the data. Select the sample file from File → Open. MerQur auto-detects column types.
Select the analysis. From the left side select GAM (Generalized Additive Models).
Panel assignments (form fields in the program):
- Target Column:
okul_id - predictors:
['ogrenci_id', 'calisma_saat'] - family:
gaussian - n_splines:
10 - lam:
0.6
Optional settings. Effect size ✓ · 95% confidence interval ✓ · Assumption checks (automatic).
▶ Run — click the button. Results are produced automatically as a table + chart.
📄 Export to Word. APA 7-formatted report with italic statistical symbols.
📊 Sample Dataset — Education Sciences
ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.
🎬 Example File
This analysis is demonstrated on the following example dataset for Education Sciences:
Egitim_Bilimleri/83_gam_study_achievement.xlsx
🎬 Scenario
Imagine we suspect that the relationship between how many hours students study and how well they score on a test is not a straight line. Maybe gains accelerate at first and then flatten out as study time grows. With 200 students and their weekly study_hour and test_score, a plain linear regression would miss that curvature. We use a Generalized Additive Model, which fits a smooth, flexible spline of study_hour onto test_score and lets the data reveal the true shape of the relationship instead of forcing it to be linear.
⚙️ Variable Selection
- Dependent variable: test_score
- Smooth predictor: study_hour
Data Preview (First 5 Rows)
| student_id | study_hour | test_score | school_id |
|---|---|---|---|
| 1.0 | 5.4 | 60.0 | 9.0 |
| 2.0 | 40.6 | 79.0 | 1.0 |
| 3.0 | 7.2 | 58.2 | 3.0 |
| 4.0 | 36.9 | 65.5 | 10.0 |
| 5.0 | 5.6 | 59.6 | 6.0 |
n = 200 · Columns: student_id, study_hour, test_score, school_id
📈 MerQur Output
💬 Interpretation
GAM is a flexible generalisation of linear regression: it models a variable’s effect with “smooth curves” (splines) rather than a straight line. Study’s effect on test score is often nonlinear — it may show diminishing returns (study saturation) beyond a point. GAM learns this curved pattern from the data without assuming its shape in advance; the model explains 62% of the variance. It preserves interpretability while adding flexibility: we can read from the curve where study helps most. For nonlinear but interpretable relationships in education (study-achievement, age-development), it is an ideal method.
⚠ Common Mistakes
- Misidentifying the data type (e.g., loading a categorical variable as numeric)
- Skipping assumption checks and going straight to the p-value
- Failing to report effect size — APA 7 requires both p and effect size
- Failing to apply a Type I error correction (Bonferroni/Tukey) in multiple comparisons
- Not switching to a non-parametric alternative when n is insufficient
📹 Video Walkthrough
Watch the video below for an end-to-end walkthrough of this analysis on a Education Sciences file.
▶ GAM (Generalized Additive Models) — video walkthrough
This section is part of the İleri Düzey I — Gelişmiş Regresyon Modelleri video (8 analyses in one video). The link below jumps straight to 1:57, where this analysis begins. Narration is in Turkish.
🧪 Natural Sciences & Mathematics · 🏛 Architecture, Planning & Design · ⚙ Engineering · 🏥 Health Sciences · 📊 Social, Humanities & Admin Sciences · 🏃 Sport Sciences · 🌾 Agriculture, Forestry & Aquatic
📚 If You Used This Analysis, Cite MerQur
If you performed this analysis using MerQur in a scientific study, please use the citation below as part of your academic citation obligations (APA 7):
Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001
For BibTeX, RIS, EndNote and the English citation form: all citation formats →
- American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).
- Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). Sage.
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.