Log-Linear Models

Categorical · Multivariate

Log-Linear 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?

Log-Linear Models automatically perform all required assumption checks (normality, homogeneity of variance, etc.) for the relevant data type in the background and present the results with a clear table + chart. Automatic interpretation in 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 Log-Linear Models.

Panel assignments (form fields in the program):

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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/27_log_linear_sex_sound_university.xlsx

🎬 Scenario

Suppose we want to understand how three categorical variables jointly relate to one another in a survey of 90 students. We recorded each student’s sex (female/male), the noise level they study in (low/high), and whether they are an avid university reader (yes/no). Rather than testing a single pairwise association, we want to model the full pattern of associations and interactions among all three variables at once. Log-Linear Analysis is suited to this because it models the cell frequencies of the multi-way contingency table and reveals which main effects and interactions are needed to explain the data.

⚙️ Variable Selection

Factor 1: sex (female/male)
Factor 2: sound (low/high)
Factor 3: university_reader (no/yes)

Data Preview (First 5 Rows)

student_id	sex	sound	university_reader
1	female	low	no
2	female	low	no
3	female	low	no
4	female	low	no
5	female	low	no

n = 90 · Columns: student_id, sex, sound, university_reader

📈 MerQur Output

LOG-LINEAR MODELS RESULT ───────────────────────────────────────────── Best model AIC = 46.72 Pearson chi-square = 0.0 (model fits the data perfectly) Factors: sex x socio-economic level x university preference

💬 Interpretation

We analysed the contingency structure formed jointly by three categorical variables — sex, socio-economic level and university preference — with a log-linear model. The selected model fits perfectly (Pearson chi-square = 0), with AIC = 46.72 as the most parsimonious model. Log-linear analysis lets us untangle interactions among more than two categorical variables (which are dependent, which interaction is significant) — it is like ANOVA for categorical data. It is powerful for summarising multi-way demographic/preference relationships in education.

⚠ 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.

▶ Log-Linear Models — video walkthrough

This section is part of the Kategorik Veri Analizleri video (7 analyses in one video). The link below jumps straight to 9:34, where this analysis begins. Narration is in Turkish.

▶ Watch this analysis (9:34) 📺 All videos

🔀 The same analysis in other disciplines:
🧪 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 →

Sources:

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.