The conditional model for FSFIT including fixed-effectes and randome effects

conditional model

1. Conditional model :

2. The model shows that time increases the outcome by almost 1 unit, and treatment group slightly lowers it by
0.18 units. Both effects are significant.
In terms of variability, there’s substantial variation in the baseline outcome (intercept) across subjects, with a
variance of 13.13. Even after accounting for that, there’s still some within-subject variability (residual variance of
0.76).
Lastly, the likelihood ratio test shows that including random effects makes the model a much better fit compared to
a simpler linear model.

Visualization:

4. • Top-Left Plot: All groups show improvements over time, but the amount of change varies a bit between groups.
• Top-Right Plot: On average, all groups improve with time, with some groups showing stronger gains.
• Bottom-Left Plot: The residuals mostly follow a normal distribution, with a few exceptions at the extremes.
• Bottom-Right Plot: The errors are similar across all groups, and the median error is close to zero, meaning the
model fits pretty well.

5. • Time has a strong, positive effect, increasing the outcome by about 1 unit with each passing time unit.
• Group doesn't have a significant effect.
• Treatment group slightly lowers the outcome by about 0.19 units, and this is a significant effect.
• There's a lot of variation between individuals in their starting points (baseline) and how time affects them.
People with higher starting points tend to see less improvement over time.

[• var(time): The effect of time varies across individuals, with some seeing more impact than others. The
variation is small but there’s some uncertainty.
• var(_cons): There’s a big difference in starting points (baseline outcomes) between individuals.
• cov(time, _cons): People who start higher tend to have smaller improvements over time, and this negative
relationship is significant.
• var(Residual): There’s still some variation in outcomes within individuals that the model hasn’t fully explained
• The model with random effects fits the data much better than a basic linear model.]

6. The LR test shows that the mixed-effects model is a much better fit than a simple linear model. The test statistic is
461.32, with a p-value of 0.0000, meaning the mixed model works significantly better

Graphs:

7. • Top-left panel: Shows individual group changes over time. Pilates, Mindfulness, and Combination groups
improve, while the Control group remains flat.
• Top-middle panel: Displays average predicted outcomes. The intervention groups improve, while the Control
group stays steady.
• Top-right panel: A Q-Q plot of residuals that mostly follows the straight line, indicating normal distribution—
good for the model.
• Bottom-left panel: Another Q-Q plot confirming that residuals fit a normal distribution with minor deviations.
• Bottom-middle panel: Shows a negative trend between random effects, indicating that individuals with higher
starting scores improve less over time.
• Bottom-right panel: Boxplots of residuals for each group show similar distributions with no extreme outliers,
indicating a good model fit.

9. Fixed Effects:
1. Time: The effect of time on the outcome is 0.578, but it’s not significant (p = 0.719). This means time
doesn't really impact the results.
2. t2: This term has a coefficient of 0.069, and it's also not significant (p = 0.795). So, it doesn’t have a
meaningful effect.
3. Group: The group variable has a coefficient of -0.309, which is not significant (p = 0.729). This indicates no
significant difference between groups.
4. tg: The coefficient is 0.136, but it’s not significant (p = 0.817), suggesting that this interaction doesn't impact
the outcome.
5. t2g: With a coefficient of -0.054, this term is also not significant (p = 0.581), meaning it doesn’t contribute
to the model.
6. Constant (_cons): The intercept is significant (p = 0.000) at 24.486, showing the average starting point for
the outcome measure.
Random Effects:
• Variance of the intercept (var(_cons)): The variance is 13.114, indicating that there is a lot of variability in
baseline outcomes among subjects. This is significant.

10. • Residual variance (var(Residual)): This is 0.760, showing there’s still some variability in the data that the
model doesn’t explain.
LR Test:
• The LR test statistic is 455.87 with a p-value of 0.0000. This means the mixed-effects model is a much better
fit for the data compared to a simpler linear model without random effects.
Summary:
In summary, the fixed effects show no significant relationships, while the random effects indicate variability
among subjects. The mixed model is preferred over a linear model because it fits the data better.
Include baseline:

12. Model Overview:
• Observations: The model includes 288 data points from 96 groups, with each group having about 3
observations on average.
• Model Fit: The Wald chi-squared statistic is 1044.06 with a p-value of 0.0000. This means the model
significantly predicts the outcome.
Fixed Effects:
1. fsfit1: This variable has a coefficient of 0.918 and is statistically significant (p < 0.001). It means that as
fsfit1 increases by 1 unit, the outcome increases by about 0.918 units.
2. Time: The coefficient is 0.928, but it’s not significant (p = 0.415). So, while time appears to have a positive
effect, we can’t be confident about it.
3. Group: This has a coefficient of -0.670 and is not significant (p = 0.637), indicating group does not
significantly impact the outcome.
4. tg: The coefficient is 0.226, also not significant (p = 0.599), meaning it doesn’t have a meaningful effect.

13. 5. tf1: This variable has a coefficient of 0.0025 and is not significant (p = 0.956), suggesting no effect on the
outcome.
6. gf: With a coefficient of 0.0403 and a p-value of 0.467, it shows no significant relationship with the
outcome.
7. tgf: The coefficient is -0.0166 and not significant (p = 0.322), indicating no significant interaction.
8. Constant: The intercept is 0.623 and not significant (p = 0.869), which tells us the expected outcome when
all other variables are zero.
Random Effects:
• Variance of Time: Estimated at 0.1074, this shows there’s some variability in how time affects different
subjects, but we have some uncertainty here.
• Variance of the Intercept: This is 1.5948, showing significant differences in baseline outcomes among
individuals.
• Covariance: The negative covariance of -0.2532 suggests that individuals with higher baseline outcomes
may have smaller effects from time, but it’s uncertain.
• Residual Variance: This is 0.6291, meaning there’s still some unexplained variability left after accounting
for the predictors.
LR Test:
• The LR test statistic is 94.65 with a p-value of 0.0000. This shows that our mixed-effects model fits the data
much better than a simpler model without random effects.
Summary:
In summary, fsfit1 is a significant predictor of the outcome, while other fixed effects are not significant. The
random effects indicate variability in both baseline outcomes and the effect of time. Overall, the mixed-effects
model is a better fit for the data.

14. Drop tgf

15. Model Overview:
• Data: Analyzed 288 observations across 96 groups, averaging 3 per group.
• Fit: The model is significant with a Wald chi-squared value of 1042.29 (p < 0.001), indicating it effectively
predicts the outcome.
Fixed Effects:
1. fsfit1: Increases the outcome by 1.032 units (p < 0.001).
2. Time: Increases the outcome by 1.955 units (p < 0.001).
3. Group: No significant effect (coefficient: 0.522, p = 0.489).
4. tg: Decreases the outcome by 0.195 units (p = 0.001).
5. tf1: Slight decrease in outcome by 0.038 units (p = 0.029).
6. gf: No significant effect (coefficient: -0.007, p = 0.816).
7. Intercept: The expected outcome when all predictors are zero is -2.292 (not significant).
Random Effects:
• Time Variance: Indicates variability in how time affects individuals (estimate: 0.1117).

16. • Intercept Variance: Shows significant variability in baseline outcomes (estimate: 1.6295).
• Residual Variance: Some unexplained variability remains (estimate: 0.6291).
LR Test:
• The LR test confirms that the mixed-effects model fits the data significantly better than a simpler model
(chi-squared: 94.15, p = 0.0000).
Summary:
In short, fsfit1 and time are strong predictors, tg and tf1 also show significant effects, and the mixed model
is a good fit for the data.


Drop gf

18. 1. fsfit1:
o Effect: For each unit increase in fsfit1fsfit1fsfit1, the outcome increases by 1.016 units. This effect is
very strong (p < 0.001).
2. Time:
o Effect: Each unit increase in time leads to a 1.955-unit increase in the outcome. This is also a
significant positive effect (p < 0.001).
3. Group:
o Effect: The effect of the group variable is 0.352, but it's only marginally significant (p = 0.074). This
suggests some differences between groups, but we can't confirm them yet.
4. tg:
o Effect: Each unit increase in tgtgtg decreases the outcome by 0.195 units (p = 0.001). This shows a
significant negative impact.
5. tf1:
o Effect: Each unit increase in tf1tf1tf1 results in a slight decrease of 0.038 units in the outcome (p =
0.029), which is also significant.
6. Intercept:
o Value: The intercept is -1.877, but it is not significant (p = 0.225). It reflects the expected outcome
when all other predictors are zero.
Random Effects:
• Variability:
o There is some variability in how time affects the outcome (variance = 0.1117).
o There's substantial variability in baseline outcomes across groups (variance = 1.6203).
o The negative covariance of -0.2637 indicates that as time increases, the baseline outcomes tend to
decrease slightly.
Conclusion from the LR Test:

19. • The LR test shows the mixed-effects model is significantly better than a simpler linear model (chi-squared =
94.32, p < 0.001).
Summary:
In summary, the model highlights that fsfit1fsfit1fsfit1 and time have strong positive effects on the outcome, while
tgtgtg and tf1tf1tf1 have significant negative effects. The analysis also accounts for variability between subjects,
confirming the importance of the factors included in the model. We dropped gfgfgf since it wasn’t significant,
allowing us to focus on these key findings.