Purpose

Public preview: This page shows the analysis output, figures, timing and model guidance, and dynamic reporting example without exposing the underlying R code. The paid version includes the complete editable R Markdown source, reusable diary module, all analysis code, synthetic scheduled and observed data, documentation, and exported results.

Daily diary and intensive longitudinal studies repeatedly measure changing experiences in everyday life. Their main advantage is the ability to study within-person processes: for example, whether a student reports more negative affect than usual on days when stress is higher than that student’s own average.

This workflow distinguishes those questions from between-person comparisons. It audits the person-by-day structure, separates within-person and between-person effects, respects calendar gaps when constructing lags, evaluates random slopes and serial dependence, and treats temporal ordering as evidence about sequence rather than proof of causation.

The included data are entirely synthetic. They model unequal diary completion, a short linear time trend, weekday patterns, stable person differences, within-person fluctuations, random slopes, and affect carryover. The values and findings do not describe real doctoral students.

Scope and learning outcomes

After completing the example, the user should be able to:

  • distinguish intensive longitudinal questions from ordinary wave-based change questions;
  • audit scheduled and observed person-days, duplicates, order, gaps, compliance, and usable occasions;
  • quantify within-person variation before fitting a within-person model;
  • use person-mean centering to separate within-person and between-person associations;
  • fit unconditional, concurrent, next-day lagged, and random-slope models;
  • evaluate time trends, weekday patterns, residuals, and an AR(1) sensitivity model;
  • visualize predicted within-person associations and individual trajectories; and
  • write a cautious results section that documents missingness, timing, uncertainty, and limits on causal claims.

The example uses daily observations. Multiple prompts per day, irregular continuous time, categorical outcomes, location or sensor streams, dynamic structural equation models, multilevel vector autoregression, and latent state-space models require extensions.

Diary models versus ordinary repeated measures

Feature Ordinary repeated measures or growth model Daily diary or intensive longitudinal model
Typical occasions A small number of planned waves Many closely spaced observations
Primary focus Mean change and individual growth Short-term within-person processes and carryover
Timing Often common across participants Completion times and gaps may differ
Dependence Random effects often central Random effects plus serial dependence may matter
Missingness Missing waves Unequal compliance, bursts, missed days, delayed responses
Predictors Often time invariant or wave specific Frequently time varying and person-mean centered

User settings

Simulate and import the example

Structure, timing, and compliance audit

Person-day integrity

check result
Scheduled person-days 2520
Completed person-days 2001
Unique participants scheduled 180
Unique participants observed 180
Duplicate observed person-days 0
Records out of date order 0

The analysis requires one record per participant per intended day. Resolve duplicate dates from source metadata rather than silently retaining the first row. Sort by participant and actual date before constructing lags.

Compliance and missing days

participants mean_days median_days minimum_days maximum_days below_threshold mean_compliance
180 11.117 11 3 14 1 0.794

A threshold is a planning and sensitivity decision, not a universal exclusion rule. Mixed models can use unequal numbers of observations, but participants with very few records contribute little information about within-person associations and random slopes.

Gaps and weekday completion

Within-person variability

variable between_person_sd median_within_person_sd people_with_zero_or_undefined_variance people_observed
stress 0.853 0.685 0 180
sleep 0.500 0.622 0 180
coping 0.540 0.622 0 180
positive_affect 0.435 0.674 0 180
negative_affect 1.038 0.672 3 180

A within-person predictor needs within-person variation. A variable can vary greatly across people while remaining nearly constant within each person. Inspect the number of people with zero or undefined personal variance before fitting person-specific slopes.

Prepare within-person and between-person components

stress_wp sleep_wp coping_wp
0 0 0

The within-person stress term asks whether affect changes on days when a participant reports more stress than their own observed average. The between-person stress term asks whether participants with higher average stress differ from participants with lower average stress. These are different estimands and can have different magnitudes or directions.

Grand-mean centering a time-varying predictor does not create this separation. Person means should be interpreted cautiously when compliance is low or the diary window poorly represents a person’s usual experience.

Unconditional model and intraclass correlation

between_person_variance within_person_variance ICC
1.028 0.482 0.681

The ICC describes the proportion of unconditional outcome variance attributable to stable differences between participants during this study window. It does not indicate the reliability of an individual diary entry and does not determine whether a multilevel model is needed by itself.

Concurrent multilevel model

effect term estimate std.error statistic df p.value conf.low conf.high
fixed (Intercept) 1.905 1.115 1.709 177.778 0.089 -0.295 4.106
fixed stress_wp 0.422 0.024 17.846 214.219 0.000 0.375 0.468
fixed stress_pm 0.644 0.086 7.455 178.895 0.000 0.474 0.815
fixed sleep_wp -0.201 0.022 -9.334 1803.797 0.000 -0.243 -0.159
fixed sleep_pm -0.131 0.132 -0.990 177.356 0.324 -0.391 0.130
fixed coping_wp -0.159 0.021 -7.633 1794.265 0.000 -0.200 -0.118
fixed coping_pm -0.115 0.136 -0.848 177.977 0.397 -0.383 0.153
fixed day_c -0.033 0.003 -9.474 1812.397 0.000 -0.040 -0.026
fixed weekend -0.046 0.031 -1.491 1812.461 0.136 -0.108 0.015
effect group term estimate conf.low conf.high
ran_pars participant_id sd__(Intercept) 0.854 NA NA
ran_pars participant_id cor__(Intercept).stress_wp 0.323 NA NA
ran_pars participant_id sd__stress_wp 0.157 NA NA
ran_pars Residual sd__Observation 0.556 NA NA
converged singular observations participants
TRUE FALSE 2001 180

The random stress slope allows the within-person stress association to differ across participants. A small estimated slope variance can reflect true similarity, inadequate occasions, limited within-person variation, or weak information in a 14-day design. Do not remove the slope solely to obtain a simpler-looking table.

Calendar-aware next-day model

observed_records records_with_previous_observation records_with_valid_consecutive_day_lag
2001 1821 1505
effect term estimate std.error statistic df p.value conf.low conf.high
fixed (Intercept) 1.316 0.726 1.814 75.672 0.074 -0.129 2.762
fixed lag1_stress_wp 0.142 0.028 4.977 1336.534 0.000 0.086 0.197
fixed lag1_sleep_wp -0.087 0.028 -3.057 1212.782 0.002 -0.142 -0.031
fixed lag1_coping_wp -0.041 0.027 -1.503 1186.103 0.133 -0.094 0.012
fixed lag1_negative_affect 0.346 0.026 13.506 862.961 0.000 0.296 0.396
fixed stress_pm 0.442 0.059 7.515 86.825 0.000 0.325 0.558
fixed sleep_pm -0.108 0.086 -1.260 75.043 0.211 -0.280 0.063
fixed coping_pm -0.068 0.088 -0.773 75.805 0.442 -0.244 0.108
fixed day_c -0.023 0.005 -4.782 1242.917 0.000 -0.033 -0.014
fixed weekend -0.146 0.039 -3.732 1199.049 0.000 -0.222 -0.069

The lag helper assigns a prior-day value only when two observed entries are exactly one calendar day apart. Carrying Friday’s value into Monday and calling it a one-day lag would change the estimand. The lagged model predicts current negative affect from the preceding observed calendar day while adjusting for prior negative affect and stable person means.

Time, weekday, and autocorrelation checks

Weekday sensitivity

term npar AIC BIC logLik minus2logL statistic df p.value
model_concurrent 13 4001.731 4074.549 -1987.866 3975.731 NA NA NA
model_weekday 18 4009.297 4110.122 -1986.648 3973.297 2.434 5 0.786

The day trend captures gradual change across the study window. Weekday indicators capture recurring calendar patterns. Neither adjustment replaces substantive modeling of events such as deadlines, holidays, or intervention exposure.

Continuous-time AR(1) sensitivity model

model call Model df AIC BIC logLik Test L.Ratio p-value
model_lme_independent lme.formula(fixed = negative_affect ~ stress_wp + stress_pm + sleep_wp + sleep_pm + coping_wp + coping_pm + day_c + weekend, data = ar_data, random = ~1 | participant_id, method = “ML”, na.action = na.omit, control = lmeControl(opt = “optim”)) 1 11 4015.517 4077.133 -1996.759 NA NA
model_lme_ar1 lme.formula(fixed = negative_affect ~ stress_wp + stress_pm + sleep_wp + sleep_pm + coping_wp + coping_pm + day_c + weekend, data = ar_data, random = ~1 | participant_id, correlation = corCAR1(value = 0.2, form = ~day | participant_id), method = “ML”, na.action = na.omit, control = lmeControl(opt = “optim”, maxIter = 200, msMaxIter = 200)) 2 12 3954.129 4021.346 -1965.065 1 vs 2 63.388 0

The continuous-time AR(1) structure uses the actual day gaps and lets residual correlation decay across longer intervals. It is a sensitivity model here because the random-slope model and autocorrelation model use different random-effect structures. Studies with timestamps inside each day should use the actual observation times and may need a model designed for irregular continuous time.

Residual diagnostics

Residual plots can reveal nonlinearity, unequal variance, heavy tails, and influential observations. They do not establish that the model is correctly specified. Also inspect participants with unusual trajectories and conduct sensitivity analyses that are justified by the measurement scale and design.

Visualize within-person processes

Predicted within-person stress effect

Individual trajectories

Faceted trajectories show heterogeneity, bursts, gaps, and possible reactivity that aggregate curves can hide. The selected participants are illustrative and must not replace a systematic influence review.

Planning and simulation-based power

simulations estimated_power mean_estimate monte_carlo_se
50 0.64 0.115 0.068

Power depends jointly on participants, usable occasions per participant, compliance, within-person predictor variance, outcome reliability, random-effect variation, serial dependence, and the estimand. The small simulation above is a reproducible demonstration, not a study-specific power analysis. A defensible plan should simulate the intended model using plausible parameters, missingness, timing, and decision rules, then repeat enough times to make Monte Carlo error acceptably small.

Adding participants generally improves between-person estimates and stabilizes random effects. Adding occasions can improve within-person estimates, but only when participants complete them and the added days capture meaningful variation. A long protocol with poor adherence can be less informative than a shorter, well-designed protocol.

Dynamic results text

Across 180 participants, 2001 of 2520 scheduled person-days were completed (79.4%). Participants completed a median of 11 days (range 3-14). The unconditional ICC for negative affect was 0.681, indicating that 68.1% of its unconditional variance was between participants during the diary window. In the concurrent random-slope model, a one-unit increase in stress relative to a participant’s own mean was associated with a 0.422-unit change in same-day negative affect (SE = 0.024, p < .001). The between-person stress association was 0.644 (p < .001), demonstrating why the two levels should not be combined. In the calendar-aware lagged model, prior-day stress relative to the participant’s mean was associated with a 0.142-unit change in current negative affect after adjustment for prior negative affect and the other listed covariates (p < .001). The continuous-time AR(1) sensitivity model estimated a residual correlation of 0.241 across a one-day interval. These temporal associations do not establish a causal effect of stress because time-varying confounding, measurement timing, carryover, and selective completion remain possible.

Reporting checklist

  • Describe recruitment, prompt schedule, response window, reminders, incentives, and study dates.
  • Report scheduled and completed observations, overall compliance, the distribution of completed days, gaps, duplicates, and exclusions.
  • State whether timestamps or scheduled day labels defined temporal order.
  • Document each centering decision and distinguish within-person from between-person coefficients.
  • Explain how lags were created and how missed days were handled.
  • Report fixed effects, uncertainty intervals, random effects, convergence, singularity checks, and residual diagnostics.
  • Describe time trends, weekday or cyclical effects, and the treatment of serial dependence.
  • Show predicted within-person associations and representative trajectories without implying that selected cases are typical.
  • Report missing-data assumptions and sensitivity analyses.
  • Avoid causal language unless the design and identifying assumptions justify it.
  • Archive a de-identified analysis file, code, package versions, seeds, and decision log when permitted.

When this model is not enough

Use a different or extended model when the outcome distribution is not approximately continuous and Gaussian, observation timing is highly irregular, multiple processes influence each other dynamically, measurement error is central, intensive observations are nested in couples or teams, carryover varies nonlinearly over continuous time, or the research question concerns latent states and transitions. Consider generalized mixed models, location-scale models, continuous-time models, multilevel vector autoregression, dynamic structural equation models, state-space models, or latent transition analysis as appropriate.

External validation and replication remain essential. A 14-day window can describe processes in that period; it does not guarantee that the same within-person association holds in another semester, clinical phase, institution, or population.

Export analysis-ready results

References and further study

  • Bolger, N., & Laurenceau, J.-P. (2013). Intensive Longitudinal Methods. Guilford Press.
  • Curran, P. J., & Bauer, D. J. (2011). The disaggregation of within-person and between-person effects in longitudinal models. Annual Review of Psychology, 62, 583-619.
  • Hoffman, L. (2015). Longitudinal Analysis: Modeling Within-Person Fluctuation and Change. Routledge.
  • McNeish, D., & Hamaker, E. L. (2020). A primer on two-level dynamic structural equation models for intensive longitudinal data. Psychological Methods, 25, 610-635.