Linear Mixed Models (LMM)
Linear Mixed Models (LMM) is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Natural Sciences & Mathematics 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?
Linear Mixed Models (LMM) automatically performs, in the background, all the assumption checks required for the relevant data type (normality, homogeneity of variance, etc.) and presents the results with a clear table and 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 Natural Sciences & Mathematics 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 Linear Mixed Models (LMM).
Panel assignments (form fields in the program):
- Dependent Variable:
absorbans - fixed_effects:
['zaman_saat'] - interactions:
[] - group_var:
ornek_id - random_slope:
None - method:
REML
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 — Natural Sciences & Mathematics
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 Natural Sciences & Mathematics:
Fen_Matematik/53_lmm_sample_time.xlsx
🎬 Scenario
We model repeatedly measured absorbance taking sample as a random effect. For repeated/nested data, LMM is appropriate.
⚙️ Variable Selection
- Dependent variable: absorbance
- Predictor(s): time_hour
- Cluster: sample_id (random)
- >> ADVANCED PARAMETERS (optional in the form — what they do):
- Nakagawa marginal R-squared (fixed effects) and conditional R-squared (fixed + random), beside ICC.
Data Preview (First 5 Rows)
| sample_id | time_hour | absorbance |
|---|---|---|
| 1.0 | 24.0 | 0.656 |
| 1.0 | 48.0 | 0.749 |
| 1.0 | 72.0 | 0.766 |
| 1.0 | 96.0 | 0.793 |
| 2.0 | 24.0 | 0.383 |
n = 200 · Columns: sample_id, time_hour, absorbance
📈 MerQur Output
💬 Interpretation
We modeled absorbance measured repeatedly in the same samples, taking sample identity as a random effect. ICC = 0.76 is high: most of the absorbance variability comes from between-sample differences, while within-sample repeats are similar. LMM correctly handles dependency in nested/repeated (measurements within sample) data; it solves the “independence” assumption that ordinary regression violates via random effects. In the lab it is the right choice for repeated/time-series measurement data. >> ADVANCED PARAMETERS (optional in the form — what they do): – Nakagawa marginal R-squared (fixed effects) and conditional R-squared (fixed + random), beside ICC.
⚠ 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 Natural Sciences & Mathematics file.
▶ Linear Mixed Models (LMM) — video walkthrough
This section is part of the Regresyon video (12 analyses in one video). The link below jumps straight to 12:05, where this analysis begins. Narration is in Turkish.
🎓 Education Sciences · 🏛 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.