Research method
Mixed-Effects Model
8 studies
A mixed-effects (multilevel) model includes fixed effects for the contrasts of interest and random effects for clustering or repeated measures — the same person at 6 and 12 weeks, the same household, the same activity-trial participant's weekly wear. Longitudinal trials often pair mixed models with intention-to-treat so that incomplete follow-up still contributes. A significant time slope or intervention×time term is a modelled average trajectory, not proof that a missing control group would have been flat.
mHealth papers reach for mixed models when PHQ-9, WEMWBS, MVPA or HbA1c is measured more than once and people drop in and out. It answers 'after accounting for within-person correlation, did assignment or time shift the outcome?' Its main limitation is that the random-effects structure does not create a control arm, does not fix 73.5% versus 26.9% attrition, and does not turn a 42-person Fitbit subsample into a confirmatory trial.
Studies
8
Findings
5
7 supporting · 0 challenging · 0 qualifying citations
Open tensions
2
Currently
What we know
- MoodGYM's primary analysis was an ITT mixed model of WEMWBS at baseline, 6 and 12 weeks in 3,070 randomised NHS Choices users. The intervention×time interaction was highly significant: adjusted differences favoured the programme by about 2.5 points at 6 weeks and 2.9 at 12 weeks (≈Cohen d 0.34). Attrition was 73.5% in the intervention arm versus 26.9% in wait-list control — a missing-data threat the mixed model does not erase.
- Repeated-measures RCTs in this set move behaviour or symptoms while the stimulus is on. A 50-day Facebook walking programme increased walking by about 155 min/week (P < .001) with 87.3% retention, but between-group advantages were gone three months after the app ended. Adjunctive Kokoro-app CBT produced about a 2.5-point PHQ-9 advantage at week 9 (SMD 0.40) among 164 randomised participants, without a significant remission difference.
- Glucose Buddy plus weekly educator texts in 72 adults with type 1 diabetes produced a significant HbA1c decrease versus usual care to 9 months; usage frequency did not clearly mediate that change. A mixed model can separate average glycaemic change from a usage mediator and still leave open whether the app would work without the texts.
- Single-arm and exploratory mixed-model papers describe trajectories without a randomised comparator. Among 105 IntelliCare users enrolled at PHQ-9 ≥10 and/or GAD-7 ≥8, paired outcomes improved and 37% reached PHQ-9 <5 and 42% GAD-7 <5 by end of treatment. Among 42 cancer survivors in a Fitbit subsample, mean wear was 6.2 of 7 days weekly and intervention MVPA rose from 93.8 to 195.3 min/week — use patterns, not a Fitbit-only causal test.
- Not every mixed-effects paper is an mHealth outcome trial. A British Columbia COVID-19 vaccine-intention survey found 79.8% somewhat or very likely to vaccinate; respondents skewed female, white and highly educated, with mean age about 52. Household clustering can justify random effects, but intention is not uptake and the sample is not a random draw of the province.
Largest unresolved question
A mixed model with a randomised control (MoodGYM, Kokoro-app, Facebook walking, Glucose Buddy) answers a different question from a mixed model of change inside one arm (IntelliCare field trial, Fitbit wear). Significant PHQ-9/GAD-7 improvement to 37%/42% below 5, or MVPA doubling from 93.8 to 195.3 min/week, can be expectancy, concurrent care, or the surrounding activity trial. Those papers do not licence the same causal sentence as a 2.5-point randomised PHQ-9 gap.
Procedure
How it works
The main stages of the method. Specific protocols and analysis choices vary between studies.
Identify clustering or repeated measures
The same person at 6 and 12 weeks, the same household, or weekly wear from one activity-trial participant. Random effects exist to absorb that correlation; they do not by themselves make a cluster-randomised trial.
Write fixed effects for the contrast
Assignment, time, and often an intervention×time term are the scientific contrast. A significant slope is a modelled average trajectory, not proof that a missing control group would have been flat.
Fit random effects for the clustering
Intercepts or slopes vary by person, household, or other cluster. Longitudinal trials often pair this with intention-to-treat so incomplete follow-up still contributes.
Estimate the trajectory
The output is a change in PHQ-9, WEMWBS, MVPA, or HbA1c after accounting for within-person correlation. A one-arm field trial and a randomised mixed/ITT contrast are not the same question.
Do not treat the model as a missing control arm
A mixed model answers whether assignment or time shifted the outcome after within-person correlation. It does not create a control, does not fix unequal attrition, and does not turn a small wear subsample into a confirmatory trial.
Common misconceptions
An ITT mixed model solves large, unequal dropout.
It uses the incomplete records it has. MoodGYM still compared arms with 73.5% versus 26.9% attrition. If people who leave differ in well-being, the intervention×time term can be biased even though the analysis is labelled ITT.
If PHQ-9 falls significantly over 8 weeks in a mixed model, the app caused the improvement.
IntelliCare's field trial had no control group, so expectancy and concurrent care remain explanations for 37% reaching PHQ-9 <5. Kokoro-app's 2.5-point gap is the randomised mixed/ITT contrast in this set.
Random effects mean the study was a cluster-randomised trial.
Random effects can capture repeated measures in an individually randomised app trial, wear days in a 42-person subsample, or household clustering in a vaccine-intention survey (79.8% likely). Cluster randomisation is a design choice, not a synonym for mixed models.
Related
Claim ledger
What the evidence shows
Drawn from 8 studies in this library. Mix labels say which citation roles are present; they are not a strength score. Supports means evidence for a finding; Challenges means evidence against a stated position; Qualifies marks scope.
MoodGYM's primary analysis was an ITT mixed model of WEMWBS at baseline, 6 and 12 weeks in 3,070 randomised NHS Choices users. The intervention×time interaction was highly significant: adjusted differences favoured the programme by about 2.5 points at 6 weeks and 2.9 at 12 weeks (≈Cohen d 0.34). Attrition was 73.5% in the intervention arm versus 26.9% in wait-list control — a missing-data threat the mixed model does not erase.
Repeated-measures RCTs in this set move behaviour or symptoms while the stimulus is on. A 50-day Facebook walking programme increased walking by about 155 min/week (P < .001) with 87.3% retention, but between-group advantages were gone three months after the app ended. Adjunctive Kokoro-app CBT produced about a 2.5-point PHQ-9 advantage at week 9 (SMD 0.40) among 164 randomised participants, without a significant remission difference.
Study Role Design N Population Outcome Facebook team walking RCT Supports RCT50-day Facebook app + pedometer vs wait-list; teams of friends N=110 · 51 intervention, 59 control Insufficiently active adults organized in Facebook friend teams Self-reported MVPA/walking at 8 and 20 weeks Can a CBT phone app help stubborn depression? Supports RCTKokoro-app smartphone CBT plus antidepressant switch vs medication change alone N=164 · ITT; primary outcome at week 9 in 163/164 (99.4%) Adults in Japan with antidepressant-refractory major depression PHQ-9 at week 9 Glucose Buddy plus weekly educator texts in 72 adults with type 1 diabetes produced a significant HbA1c decrease versus usual care to 9 months; usage frequency did not clearly mediate that change. A mixed model can separate average glycaemic change from a usage mediator and still leave open whether the app would work without the texts.
Single-arm and exploratory mixed-model papers describe trajectories without a randomised comparator. Among 105 IntelliCare users enrolled at PHQ-9 ≥10 and/or GAD-7 ≥8, paired outcomes improved and 37% reached PHQ-9 <5 and 42% GAD-7 <5 by end of treatment. Among 42 cancer survivors in a Fitbit subsample, mean wear was 6.2 of 7 days weekly and intervention MVPA rose from 93.8 to 195.3 min/week — use patterns, not a Fitbit-only causal test.
Study Role Design N Population Outcome IntelliCare app suite field trial Supports Human experimentSingle-arm 8-week field trial of IntelliCare Android suite with low-intensity coaching N=105 · PHQ-9 ≥10 and/or GAD-7 ≥8 at enrollment Adults with elevated depression and/or anxiety symptoms PHQ-9 and GAD-7 change over 8 weeks Fitbit wear during an activity trial Supports OtherSecondary analysis of the exercise arm of a 12-week physical-activity RCT N=42 · 42 of 43 exercise-arm completers (parent RCT randomized 87) Female breast cancer survivors in a physical-activity intervention Fitbit wear adherence and ActiGraph MVPA over 12 weeks Not every mixed-effects paper is an mHealth outcome trial. A British Columbia COVID-19 vaccine-intention survey found 79.8% somewhat or very likely to vaccinate; respondents skewed female, white and highly educated, with mean age about 52. Household clustering can justify random effects, but intention is not uptake and the sample is not a random draw of the province.
Debates
Tensions and limits
Some items are genuine disagreements on the same question. Others mark different assays, populations, or outcomes.
A mixed model with a randomised control (MoodGYM, Kokoro-app, Facebook walking, Glucose Buddy) answers a different question from a mixed model of change inside one arm (IntelliCare field trial, Fitbit wear). Significant PHQ-9/GAD-7 improvement to 37%/42% below 5, or MVPA doubling from 93.8 to 195.3 min/week, can be expectancy, concurrent care, or the surrounding activity trial. Those papers do not licence the same causal sentence as a 2.5-point randomised PHQ-9 gap.
A mixed model with a randomised control (MoodGYM, Kokoro-app, Facebook walking, Glucose Buddy) answers a different question from a mixed model of change inside one arm (IntelliCare field trial, Fitbit wear). Significant PHQ-9/GAD-7 improvement to 37%/42% below 5, or MVPA doubling from 93.8 to 195.3 min/week, can be expectancy, concurrent care, or the surrounding activity trial. Those papers do not licence the same causal sentence as a 2.5-point randomised PHQ-9 gap.
- MoodGYM improves population wellbeing
- Can a CBT phone app help stubborn depression?
- IntelliCare app suite field trial
- Fitbit wear during an activity trial
Study Role Design N Population Outcome MoodGYM improves population wellbeing Supports RCTFully automated MoodGYM vs waiting-list; ITT mixed models N=3070 · Randomized NHS Choices users; high differential attrition NHS Choices website users randomized to MoodGYM or wait-list WEMWBS well-being at 6 and 12 weeks Can a CBT phone app help stubborn depression? Supports RCTKokoro-app smartphone CBT plus antidepressant switch vs medication change alone N=164 · ITT; primary outcome at week 9 in 163/164 (99.4%) Adults in Japan with antidepressant-refractory major depression PHQ-9 at week 9 IntelliCare app suite field trial Supports Human experimentSingle-arm 8-week field trial of IntelliCare Android suite with low-intensity coaching N=105 · PHQ-9 ≥10 and/or GAD-7 ≥8 at enrollment Adults with elevated depression and/or anxiety symptoms PHQ-9 and GAD-7 change over 8 weeks Fitbit wear during an activity trial Supports OtherSecondary analysis of the exercise arm of a 12-week physical-activity RCT N=42 · 42 of 43 exercise-arm completers (parent RCT randomized 87) Female breast cancer survivors in a physical-activity intervention Fitbit wear adherence and ActiGraph MVPA over 12 weeks
PaperFren reads this as a limit on how far one study travels — different assays, populations, or outcomes — not a forced fight between papers.
Durability and missingness pull in opposite directions across trials that share the modelling family. Facebook walking's 155 min/week advantage vanished after the stimulus ended despite 87.3% retention; MoodGYM's WEMWBS advantage persisted to 12 weeks on paper while 73.5% of the intervention arm had left. A student who treats 'mixed-model p < .05' as one finding will miss both limits.
Durability and missingness pull in opposite directions across trials that share the modelling family. Facebook walking's 155 min/week advantage vanished after the stimulus ended despite 87.3% retention; MoodGYM's WEMWBS advantage persisted to 12 weeks on paper while 73.5% of the intervention arm had left. A student who treats 'mixed-model p < .05' as one finding will miss both limits.
Study Role Design N Population Outcome Facebook team walking RCT Supports RCT50-day Facebook app + pedometer vs wait-list; teams of friends N=110 · 51 intervention, 59 control Insufficiently active adults organized in Facebook friend teams Self-reported MVPA/walking at 8 and 20 weeks MoodGYM improves population wellbeing Supports RCTFully automated MoodGYM vs waiting-list; ITT mixed models N=3070 · Randomized NHS Choices users; high differential attrition NHS Choices website users randomized to MoodGYM or wait-list WEMWBS well-being at 6 and 12 weeks
PaperFren reads this as a limit on how far one study travels — different assays, populations, or outcomes — not a forced fight between papers.
Timeline
How understanding moved
Study years are when the paper was published. Evidence edits are dated changes to this page's claims. Explanations are when PaperFren added a Discovery — not a claim that the science happened that day.
2026
Concept page published
Mixed-Effects Model
Change log
What changed
Dated edits to this page's evidence: studies added or removed from a claim, claims added or withdrawn, and new explanations tagged here. Coverage edits are distinct from reviewed research changes and corrections. Dates record PaperFren updates; study publication dates appear in the timeline.
- Coverage updated · Concept page published
Papers
8 studies in this library bear on Mixed-Effects Model, ordered by citations.
- Glucose Buddy app associated with improved type 1 HbA1c in a trial
Adults with poorly controlled type 1 diabetes using Glucose Buddy plus weekly educator texts lowered HbA1c versus usual care.
- IntelliCare app suite field trial
Eight weeks of IntelliCare apps plus light coaching produced large pre–post drops in depression and anxiety symptoms.
- MoodGYM improves population wellbeing
In a large UK web RCT, automated MoodGYM raised mental well-being versus wait-list control despite high intervention attrition.
- Can a CBT phone app help stubborn depression?
Adding a smartphone CBT program to a medication switch improved depressive symptoms more than switching antidepressants alone.
- Facebook team walking RCT
A 50-day team social-network pedometer program boosted walking/MVPA during the intervention, but gains were not maintained 3 months later.
- COVID-19 vaccine intention in BC
About 80% of surveyed British Columbians said they were somewhat or very likely to take a recommended COVID-19 vaccine.
- Fitbit wear during an activity trial
Survivors wore Fitbits most days and roughly doubled ActiGraph MVPA over 12 weeks in the intervention arm.
- iCBT for depression in diabetes
Unmodified clinician-supported iCBT beat treatment-as-usual on depression, anxiety, distress, and diabetes-specific distress in adults with diabetes.
Compare studies
Select 2–10 studies. Design and N are labels, not a ranking.
Nothing selected yet.
Questions
What is still open
A mixed model with a randomised control (MoodGYM, Kokoro-app, Facebook walking, Glucose Buddy) answers a different question from a mixed model of change inside one arm (IntelliCare field trial, Fitbit wear). Significant PHQ-9/GAD-7 improvement to 37%/42% below 5, or MVPA doubling from 93.8 to 195.3 min/week, can be expectancy, concurrent care, or the surrounding activity trial. Those papers do not licence the same causal sentence as a 2.5-point randomised PHQ-9 gap.
Durability and missingness pull in opposite directions across trials that share the modelling family. Facebook walking's 155 min/week advantage vanished after the stimulus ended despite 87.3% retention; MoodGYM's WEMWBS advantage persisted to 12 weeks on paper while 73.5% of the intervention arm had left. A student who treats 'mixed-model p < .05' as one finding will miss both limits.
Ask PaperFren about Mixed-Effects Model
Study this conceptflashcards and short-answer questions
MoodGYM reports an intervention×time term and WEMWBS advantages of about 2.5 and 2.9 points. What does the mixed model add, and what do the attrition figures still threaten?
The mixed model uses repeated WEMWBS measures (baseline, 6, 12 weeks) and within-person correlation so incomplete follow-up still contributes to an ITT estimate among 3,070 randomised users. Attrition of 73.5% versus 26.9% can still bias that estimate if dropout relates to well-being; wait-list controls may also inflate benefit.
Compare IntelliCare's 37% PHQ-9 <5 rate with Kokoro-app's 2.5-point randomised PHQ-9 difference. Which design supports a causal app effect, and why?
Kokoro-app randomised 164 participants to add smartphone CBT versus medication change alone, so the 2.5-point (SMD 0.40) contrast is a treatment effect on the assigned population (remission still NS). IntelliCare enrolled 105 symptomatic adults in a single arm; 37% below 5 can reflect time, coaching, concurrent care or expectancy.
The Facebook walking trial increased walking by about 155 min/week during the programme. How should a mixed-model 'success' be time-stamped?
During the 50-day stimulus, with 87.3% retention. Between-group advantages were not maintained 3 months after the app ended, so the modelled benefit is time-limited, not a self-sustaining habit.
Glucose Buddy improved HbA1c versus usual care, but usage frequency did not clearly mediate the change. What should a student conclude about 'engagement' as a mixed-model mediator?
In 72 adults followed to 9 months, the app-plus-text package moved HbA1c without a clear usage-frequency pathway. More taps are not automatically the mechanism, and the trial does not show the app would work without educator texts.