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title author date output
fitbit analysis for CSEP project
Shelby Sturrock
09/03/2022
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Fitbit analysis

Summary

This script contains a few simplified figures for the CSEP 24 hour movement guideline proof of concept paper.

Data processing steps include:

  1. First, remove participant-days of data where "TotalTimeInBed" is 0. Eliminating these records (n~500, need to confirm) also removes all participants-days with 0 total steps, 0 minutes of light physical activity and 1440 minutes of sedentary time. This step happens in the "fitbit-wrangling" file and the records are omitted from the TOP.
  2. Second, remove participant-days with less than 10 hours of wear time. Minute-level data was identified as "non-wear time" if the current minute and the previous 9 minutes each had 0 steps, missing heart rate AND were flagged as having "sedentary" intensity. If these conditions are met, all 10 minutes are flagged as "non-wear time". If at least one minute has >0 steps, non-sedentary intensity OR a heart rate value, none of the 10 minutes are flagged as non-wear time. Total non-wear minutes were then summed per participant and day, and days with > 840 minutes of non-wear time were excluded from analysis (n=3). This steps occurs within this script.
  3. Third, remove the first day of data (October 18, 2021) because the mean number of non-wear minutes across participant was an order of magnitude higher than the second highest day (~650 minutes vs. ~62 minutes), which led to artificially low light PA, and sleep, but inflated sedentary time.

Analysis includes:

  1. Scatter plot and trend (using LOESS) of each movement behaviour (a) over the study period, and (b) seperately before, during and after the intervention period.
  2. Box plot of each behaviour type before, during and after the intervention period.
  3. Trend in daily clicks (any) vs. daily minutes of each movemebt behaviour before, during and after the intervention period (where trends are illustrated using LOESS curves fit to data from each period seperately)
  4. Trend in daily clicks (on intervention content specifically) vs. daily minutes of each movement behaviour within the intervention period specifically (again using LOESS curves to illustrate trends)

Read in and format data

Read in data

daily <- read.csv("daily-TOP-CSEP.csv")
str(daily$date)
##  chr [1:3533] "2021-10-19" "2021-10-22" "2021-10-23" "2021-10-24" ...

Make sure that the intervention variable and the weekday variables are formatted as factors where the intervention periods and weekdays are ordered correctly (pre, intervention, post; monday, tuesday, etc.)

  daily$weekday<-factor(daily$weekday,
                        levels=c("Monday","Tuesday","Wednesday","Thursday","Friday","Saturday","Sunday"))
  daily$intervention<-factor(daily$intervention,levels=c("pre","intervention","post"))
  daily$date<-as.Date(daily$date)
  str(daily$weekday)
##  Factor w/ 7 levels "Monday","Tuesday",..: 2 5 6 7 1 3 4 5 6 7 ...

  str(daily$intervention)
##  Factor w/ 3 levels "pre","intervention",..: 1 1 1 1 2 2 2 2 2 2 ...

Create person-day-level for plots. Currently, the "daily" dataframe has one row per person-day-article, so if someone engages with two different articles, they have two rows in the dataframe. I want a maximum of one row per person per day for data exploration.

  dailyForPlots<-daily[!is.na(daily$totalMVPA),] %>% select(-title,-intervention_content,-featured_content,
                                                            -pubdate,-weekofpublish,
                                                            -type,-click,-engage,-clickInt,-engageInt)
  dailyForPlots<-distinct(dailyForPlots)
# tentative: remove particiapnt-days with less than 10 hours of wear time (so 14 hours or more of non-wear time)
  # 14 * 60 = 840 (840 minutes or more of non-wear time)

Recall that we've already removed (a) participant-days with 0 minutes of time in bed (n=), and (b) participant-days with <10 hours of wear time (14+ hours of non-wear time) (n=), and (c) the first day of data for all participants (October 18), since the average number of non-wear minutes across participants was 10 time greater on October 18 (659 minutes) compared to the second highest day (62.7 on December 12, the last day of data collection)

Explore total minutes of data contributed per particiant day. Should be ~1440 minutes

MVPA

Plot of minutes of MVPA per day over time

Trend over study period

Largely stable over time, slight bow (where lower at the beginning and end)

Trend before, during and after intervention

Largely stable over time, particularly during the intervention period. Slightly lower in post-period.

LPA

Plot of minutes of LPA per day over time -- overall and comparing engagers and non-engagers

Trend over study period

Slight downward trend in lightly active minutes over time (looks driven by post-period)

Trend before, during and after intervention

Largely stable over time, particularly during the intervention period. Slightly lower in post-period.

Sedentary Behaviour

Plot of minutes of SB per day over time -- overall and comparing engagers and non-engagers

Trend over study period

Slight bow (highest at beginning and end) but more or less stable over time.

Trend before, during and after intervention

Sedentary time appeared to decrease slightly during the pre-period, otherwise stable over time.

Sleep

Plot of minutes of Sleep per day over time -- overall and comparing engagers and non-engagers

Trend over study period

Sleep appears to increase slightly over time.

Trend before, during and after intervention

Fit a loess curve to each of the three periods. Appears that sleep increased during each period.

High-level: All movement behaviours over time

Plot of all movement behaviours over time

## Before During  After 
##   1156   9844   1772

Plots

Boxplot - one panel per movement behaviour

MVPA

Lightly active minutes

Sedentary time

Sleep

Line Graph - with engagement and clicks overlayed

# # MVPA
#   dailyForPlots$clickMVPA<-dailyForPlots$dayCountClickAny*(mean(dailyForPlots$totalMVPA)/mean(dailyForPlots$dayCountClickAny))
#   dailyForPlots$engageMVPA<-dailyForPlots$dayCountEngageAny*(mean(dailyForPlots$totalMVPA)/mean(dailyForPlots$dayCountEngageAny))
# 
# # Lightly Active Minutes
#   dailyForPlots$clickLPA<-dailyForPlots$dayCountClickAny*
#                           (mean(dailyForPlots$LightlyActiveMinutes)/mean(dailyForPlots$dayCountClickAny))
#   dailyForPlots$engageLPA<-dailyForPlots$dayCountEngageAny*
#                            (mean(dailyForPlots$LightlyActiveMinutes)/mean(dailyForPlots$dayCountEngageAny))
#   
# # Sedentary Behavior
#   dailyForPlots$clickSB<-dailyForPlots$dayCountClickAny*
#                           (mean(dailyForPlots$SedentaryMinutes)/mean(dailyForPlots$dayCountClickAny))
#   dailyForPlots$engageSB<-dailyForPlots$dayCountEngageAny*
#                           (mean(dailyForPlots$SedentaryMinutes)/mean(dailyForPlots$dayCountEngageAny))
#   
# # Sleep 
#   dailyForPlots$clickSleep<-dailyForPlots$dayCountClickAny*
#                             (mean(dailyForPlots$TotalTimeInBed)/mean(dailyForPlots$dayCountClickAny))
#   dailyForPlots$engageSleep<-dailyForPlots$dayCountEngageAny*
#                             (mean(dailyForPlots$TotalTimeInBed)/mean(dailyForPlots$dayCountEngageAny))

Intervention clicks during intervention period

The following figures display trends in clicks on intervention content compared to trends in each movement behaviour over the course of the intervention period. The y axis on the left concerns the movement behaviour (colored lines) and the y axis on the right concerns daily clicks on intervention content (black line).

Generate click and engagement variables that are rescaled such that the mean = mean of the respective behaviour for plotting

  dailyInt<-dailyForPlots[dailyForPlots$intervention=="intervention",]

# MVPA
  dailyInt$clickIntMVPA<-dailyInt$dayCountClickInt*
                               (mean(dailyInt$totalMVPA)/mean(dailyInt$dayCountClickInt))
  dailyInt$engageIntMVPA<-dailyInt$dayCountEngageInt*
                               (mean(dailyInt$totalMVPA)/mean(dailyInt$dayCountEngageInt))

# Lightly Active Minutes
  dailyInt$clickIntLPA<-dailyInt$dayCountClickInt*
                          (mean(dailyInt$LightlyActiveMinutes)/mean(dailyInt$dayCountClickInt))
  dailyInt$engageIntLPA<-dailyInt$dayCountEngageInt*
                           (mean(dailyInt$LightlyActiveMinutes)/mean(dailyInt$dayCountEngageInt))
  
# Sedentary Behavior
  dailyInt$clickIntSB<-dailyInt$dayCountClickInt*
                          (mean(dailyInt$SedentaryMinutes)/mean(dailyInt$dayCountClickInt))
  dailyInt$engageIntSB<-dailyInt$dayCountEngageInt*
                          (mean(dailyInt$SedentaryMinutes)/mean(dailyInt$dayCountEngageInt))
  
# Sleep 
  dailyInt$clickIntSleep<-dailyInt$dayCountClickInt*
                            (mean(dailyInt$TotalTimeInBed)/mean(dailyInt$dayCountClickInt))
  dailyInt$engageIntSleep<-dailyInt$dayCountEngageInt*
                            (mean(dailyInt$TotalTimeInBed)/mean(dailyInt$dayCountEngageInt))

Using LOESS smoother

Using multilevel models

Create a time variable (where Oct 18 = 1, Oct 19 = 2, etc.)

Clicks

(a) plot to see what emerges when data is allowed to dictate the shape. It looks as though there is at least 2 or 3 inflection points... requiring a third or fourth order factor

(b) assess models of daily intervention clicks as a function of date/time with and without higher order time parameters.

# linear, no higher order factors
  test<-lm(dayCountClickInt~nDate,data=dailyInt)
  summary(test)
## 
## Call:
## lm(formula = dayCountClickInt ~ nDate, data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.1387 -0.1196 -0.1004 -0.0813  5.9221 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.1404164  0.0162173   8.658  < 2e-16 ***
## nDate       -0.0017378  0.0006739  -2.579  0.00997 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3964 on 2459 degrees of freedom
## Multiple R-squared:  0.002697,	Adjusted R-squared:  0.002292 
## F-statistic:  6.65 on 1 and 2459 DF,  p-value: 0.009971

# linear + quadratic (nDate^2)
  test2<-lm(dayCountClickInt~nDate+I(nDate*nDate),data=dailyInt)
  summary(test2)
## 
## Call:
## lm(formula = dayCountClickInt ~ nDate + I(nDate * nDate), data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.1566 -0.1154 -0.0910 -0.0842  5.9163 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.612e-01  2.509e-02   6.423 1.59e-10 ***
## nDate            -4.641e-03  2.763e-03  -1.680   0.0932 .  
## I(nDate * nDate)  6.916e-05  6.385e-05   1.083   0.2788    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3964 on 2458 degrees of freedom
## Multiple R-squared:  0.003173,	Adjusted R-squared:  0.002362 
## F-statistic: 3.912 on 2 and 2458 DF,  p-value: 0.02012

# linear + cubic (nDate^3)
  test3<-lm(dayCountClickInt~poly(nDate,3),data=dailyInt)
  summary(test3)
## 
## Call:
## lm(formula = dayCountClickInt ~ poly(nDate, 3), data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.1412 -0.1236 -0.0941 -0.0793  5.9184 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      0.10402    0.00799  13.019  < 2e-16 ***
## poly(nDate, 3)1 -1.02216    0.39637  -2.579  0.00997 ** 
## poly(nDate, 3)2  0.42937    0.39637   1.083  0.27880    
## poly(nDate, 3)3  0.34264    0.39637   0.864  0.38744    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3964 on 2457 degrees of freedom
## Multiple R-squared:  0.003476,	Adjusted R-squared:  0.002259 
## F-statistic: 2.857 on 3 and 2457 DF,  p-value: 0.03579

# compare AIC for the four models
  extractAIC(test)
## [1]     2.000 -4552.894

  extractAIC(test2)
## [1]     3.000 -4552.068

  extractAIC(test3)
## [1]     4.000 -4550.817

(c) models, with random intercept per participant

  click<-lme4::lmer(dayCountClickInt~nDate+(1|Id),data=dailyInt)

(d) generate predicted values

  dailyInt$fit_click<-fitted(click)

(e) plot predicted value of clicks

Engagement

(a) plot to see what emerges when data is allowed to dictate the shape.

(b) assess models of daily intervention engagement as a function of date/time with and without higher order time parameters.

# linear, no higher order factors
  test<-lm(dayCountEngageInt~nDate,data=dailyInt)
  summary(test)
## 
## Call:
## lm(formula = dayCountEngageInt ~ nDate, data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.1042 -0.0868 -0.0695 -0.0537  5.9510 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.1057653  0.0131270   8.057 1.21e-15 ***
## nDate       -0.0015772  0.0005455  -2.892  0.00387 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3208 on 2459 degrees of freedom
## Multiple R-squared:  0.003389,	Adjusted R-squared:  0.002983 
## F-statistic: 8.361 on 1 and 2459 DF,  p-value: 0.003867

# linear + quadratic (nDate^2)
  test2<-lm(dayCountEngageInt~nDate+I(nDate*nDate),data=dailyInt)
  summary(test2)
## 
## Call:
## lm(formula = dayCountEngageInt ~ nDate + I(nDate * nDate), data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.1185 -0.0835 -0.0619 -0.0546  5.9463 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.224e-01  2.031e-02   6.025 1.95e-09 ***
## nDate            -3.899e-03  2.237e-03  -1.743   0.0814 .  
## I(nDate * nDate)  5.532e-05  5.168e-05   1.070   0.2845    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3208 on 2458 degrees of freedom
## Multiple R-squared:  0.003853,	Adjusted R-squared:  0.003043 
## F-statistic: 4.754 on 2 and 2458 DF,  p-value: 0.008699

# linear + cubic (nDate^3)
  test3<-lm(dayCountEngageInt~poly(nDate,3),data=dailyInt)
  summary(test3)
## 
## Call:
## lm(formula = dayCountEngageInt ~ poly(nDate, 3), data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.1156 -0.0850 -0.0614 -0.0543  5.9467 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      0.072735   0.006468  11.245  < 2e-16 ***
## poly(nDate, 3)1 -0.927710   0.320890  -2.891  0.00387 ** 
## poly(nDate, 3)2  0.343442   0.320890   1.070  0.28460    
## poly(nDate, 3)3  0.063484   0.320890   0.198  0.84319    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3209 on 2457 degrees of freedom
## Multiple R-squared:  0.003869,	Adjusted R-squared:  0.002653 
## F-statistic: 3.181 on 3 and 2457 DF,  p-value: 0.02305

# compare AIC for the four models
  extractAIC(test)
## [1]     2.000 -5593.446

  extractAIC(test2)
## [1]     3.000 -5592.593

  extractAIC(test3)
## [1]     4.000 -5590.632

(c) models, with random intercept per participant

  engage<-lme4::lmer(dayCountEngageInt~nDate+(1|Id),data=dailyInt)

(d) generate predicted values

  dailyInt$fit_engage<-fitted(engage)

(e) plot predicted values of daily engagement over time

MVPA:

(a) plot to see what emerges when data is allowed to dictate the shape.

(b) assess models of daily intervention engagement as a function of date/time with and without higher order time parameters.

# linear, no higher order factors
  test<-lm(totalMVPA~nDate,data=dailyInt)
  summary(test)
## 
## Call:
## lm(formula = totalMVPA ~ nDate, data = dailyInt)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -47.75 -32.80 -10.73  18.52 403.84 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 47.91702    1.86124  25.745   <2e-16 ***
## nDate       -0.16998    0.07734  -2.198   0.0281 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 45.49 on 2459 degrees of freedom
## Multiple R-squared:  0.001961,	Adjusted R-squared:  0.001555 
## F-statistic: 4.831 on 1 and 2459 DF,  p-value: 0.02805

# linear + quadratic (nDate^2)
  test2<-lm(totalMVPA~nDate+I(nDate*nDate),data=dailyInt)
  summary(test2)
## 
## Call:
## lm(formula = totalMVPA ~ nDate + I(nDate * nDate), data = dailyInt)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -49.59 -32.45 -10.62  18.40 404.49 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      50.054233   2.879489  17.383   <2e-16 ***
## nDate            -0.469165   0.317137  -1.479    0.139    
## I(nDate * nDate)  0.007128   0.007328   0.973    0.331    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 45.49 on 2458 degrees of freedom
## Multiple R-squared:  0.002345,	Adjusted R-squared:  0.001533 
## F-statistic: 2.888 on 2 and 2458 DF,  p-value: 0.05585

# linear + cubic (nDate^3)
  test3<-lm(totalMVPA~poly(nDate,3),data=dailyInt)
  summary(test3)
## 
## Call:
## lm(formula = totalMVPA ~ poly(nDate, 3), data = dailyInt)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -50.79 -32.42 -10.88  18.68 403.91 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      44.3572     0.9171  48.365   <2e-16 ***
## poly(nDate, 3)1 -99.9831    45.4973  -2.198   0.0281 *  
## poly(nDate, 3)2  44.2515    45.4973   0.973   0.3308    
## poly(nDate, 3)3 -26.3536    45.4973  -0.579   0.5625    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 45.5 on 2457 degrees of freedom
## Multiple R-squared:  0.002481,	Adjusted R-squared:  0.001263 
## F-statistic: 2.037 on 3 and 2457 DF,  p-value: 0.1066

# compare AIC for the four models
  extractAIC(test)
## [1]     2.00 18791.77

  extractAIC(test2)
## [1]     3.00 18792.82

  extractAIC(test3)
## [1]     4.00 18794.49

(c) models, with random intercept per participant

  mvpa<-lme4::lmer(totalMVPA~nDate+(1|Id),data=dailyInt)

(d) generate predicted values

  dailyInt$fit_mvpa<-fitted(mvpa)

(e) rescale engagement and click data for plotting with MVPA

  dailyInt$click_mvpa<-dailyInt$fit_click*
                               (mean(dailyInt$fit_mvpa)/mean(dailyInt$fit_click))
  dailyInt$engage_mvpa<-dailyInt$fit_engage*
                               (mean(dailyInt$fit_mvpa)/mean(dailyInt$fit_engage))

(f) plot predicted values of MVPA over time + predicted values of intervention clicks

Lightly active minutes:

(a) plot to see what emerges when data is allowed to dictate the shape.

(b) assess models of daily intervention engagement as a function of date/time with and without higher order time parameters.

# linear, no higher order factors
  test<-lm(LightlyActiveMinutes~nDate,data=dailyInt)
  summary(test)
## 
## Call:
## lm(formula = LightlyActiveMinutes ~ nDate, data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -201.31  -56.69   -7.46   47.46  341.07 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 212.1879     3.2366   65.56   <2e-16 ***
## nDate        -0.2689     0.1345   -2.00   0.0456 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 79.11 on 2459 degrees of freedom
## Multiple R-squared:  0.001624,	Adjusted R-squared:  0.001218 
## F-statistic: 3.999 on 1 and 2459 DF,  p-value: 0.04564

# linear + quadratic (nDate^2)
  test2<-lm(LightlyActiveMinutes~nDate+I(nDate*nDate),data=dailyInt)
  summary(test2)
## 
## Call:
## lm(formula = LightlyActiveMinutes ~ nDate + I(nDate * nDate), 
##     data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -201.70  -57.02   -7.69   47.94  341.82 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      214.33475    5.00797  42.799   <2e-16 ***
## nDate             -0.56948    0.55156  -1.032    0.302    
## I(nDate * nDate)   0.00716    0.01274   0.562    0.574    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 79.12 on 2458 degrees of freedom
## Multiple R-squared:  0.001752,	Adjusted R-squared:  0.0009396 
## F-statistic: 2.157 on 2 and 2458 DF,  p-value: 0.1159

# linear + cubic (nDate^3)
  test3<-lm(LightlyActiveMinutes~poly(nDate,3),data=dailyInt)
  summary(test3)
## 
## Call:
## lm(formula = LightlyActiveMinutes ~ poly(nDate, 3), data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -200.94  -56.52   -7.69   47.47  341.47 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      206.555      1.595 129.505   <2e-16 ***
## poly(nDate, 3)1 -158.193     79.124  -1.999   0.0457 *  
## poly(nDate, 3)2   44.452     79.124   0.562   0.5743    
## poly(nDate, 3)3  -62.432     79.124  -0.789   0.4302    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 79.12 on 2457 degrees of freedom
## Multiple R-squared:  0.002005,	Adjusted R-squared:  0.0007862 
## F-statistic: 1.645 on 3 and 2457 DF,  p-value: 0.1769

# compare AIC for the four models
  extractAIC(test)
## [1]     2.00 21515.06

  extractAIC(test2)
## [1]     3.00 21516.75

  extractAIC(test3)
## [1]     4.00 21518.13

(c) models, with random intercept per participant

  LPA<-lme4::lmer(LightlyActiveMinutes~nDate+(1|Id),data=dailyInt)

(d) generate predicted values

  dailyInt$fit_LPA<-fitted(LPA)

(e) rescale engagement and click data for plotting with LPA

  dailyInt$click_LPA<-dailyInt$fit_click*
                               (mean(dailyInt$fit_LPA)/mean(dailyInt$fit_click))
  dailyInt$engage_LPA<-dailyInt$fit_engage*
                               (mean(dailyInt$fit_LPA)/mean(dailyInt$fit_engage))

(f) plot predicted values LPA over time + predicted values of intervention clicks

Sedentary minutes:

(a) plot to see what emerges when data is allowed to dictate the shape.

(b) assess models of daily intervention engagement as a function of date/time with and without higher order time parameters.

# linear, no higher order factors
  test<-lm(SedentaryMinutes~nDate,data=dailyInt)
  summary(test)
## 
## Call:
## lm(formula = SedentaryMinutes ~ nDate, data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -709.59  -65.96   22.61  100.93  496.96 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 724.7499     6.6179 109.514   <2e-16 ***
## nDate        -0.4821     0.2750  -1.753   0.0797 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 161.7 on 2459 degrees of freedom
## Multiple R-squared:  0.001248,	Adjusted R-squared:  0.0008422 
## F-statistic: 3.074 on 1 and 2459 DF,  p-value: 0.07969

# linear + quadratic (nDate^2)
  test2<-lm(SedentaryMinutes~nDate+I(nDate*nDate),data=dailyInt)
  summary(test2)
## 
## Call:
## lm(formula = SedentaryMinutes ~ nDate + I(nDate * nDate), data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -706.03  -65.46   21.79   99.64  501.92 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      737.59567   10.23475  72.068   <2e-16 ***
## nDate             -2.28034    1.12722  -2.023   0.0432 *  
## I(nDate * nDate)   0.04284    0.02605   1.645   0.1001    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 161.7 on 2458 degrees of freedom
## Multiple R-squared:  0.002347,	Adjusted R-squared:  0.001535 
## F-statistic: 2.891 on 2 and 2458 DF,  p-value: 0.05572

# linear + cubic (nDate^3)
  test3<-lm(SedentaryMinutes~poly(nDate,3),data=dailyInt)
  summary(test3)
## 
## Call:
## lm(formula = SedentaryMinutes ~ poly(nDate, 3), data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -707.31  -65.16   21.07  101.07  505.51 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      714.653      3.259 219.290   <2e-16 ***
## poly(nDate, 3)1 -283.574    161.671  -1.754   0.0796 .  
## poly(nDate, 3)2  265.975    161.671   1.645   0.1001    
## poly(nDate, 3)3 -206.312    161.671  -1.276   0.2020    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 161.7 on 2457 degrees of freedom
## Multiple R-squared:  0.003007,	Adjusted R-squared:  0.00179 
## F-statistic: 2.471 on 3 and 2457 DF,  p-value: 0.06013

# compare AIC for the four models
  extractAIC(test)
## [1]     2.00 25035.49

  extractAIC(test2)
## [1]     3.00 25034.78

  extractAIC(test3)
## [1]     4.00 25035.15

(c) models, with random intercept per participant

  SB<-lme4::lmer(SedentaryMinutes~nDate+I(nDate*nDate)+(1|Id),data=dailyInt)

(d) generate predicted values

  dailyInt$fit_SB<-fitted(SB)

(e) rescale engagement and click data for plotting with SB

  dailyInt$click_SB<-dailyInt$fit_click*
                               (mean(dailyInt$fit_SB)/mean(dailyInt$fit_click))
  dailyInt$engage_SB<-dailyInt$fit_engage*
                               (mean(dailyInt$fit_SB)/mean(dailyInt$fit_engage))

(f) plot predicted values SB over time + predicted values of intervention clicks

Sleep minutes:

(a) plot to see what emerges when data is allowed to dictate the shape.

(b) assess models of daily intervention engagement as a function of date/time with and without higher order time parameters.

# linear, no higher order factors
  test<-lm(TotalTimeInBed~nDate,data=dailyInt)
  summary(test)
## 
## Call:
## lm(formula = TotalTimeInBed ~ nDate, data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -374.00  -60.72   -0.25   61.42  429.66 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 447.6163     4.1255 108.500   <2e-16 ***
## nDate         0.3027     0.1714   1.766   0.0776 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 100.8 on 2459 degrees of freedom
## Multiple R-squared:  0.001266,	Adjusted R-squared:  0.0008601 
## F-statistic: 3.118 on 1 and 2459 DF,  p-value: 0.07757

# linear + quadratic (nDate^2)
  test2<-lm(TotalTimeInBed~nDate+I(nDate*nDate),data=dailyInt)
  summary(test2)
## 
## Call:
## lm(formula = TotalTimeInBed ~ nDate + I(nDate * nDate), data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -375.32  -61.18   -0.54   60.36  429.76 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      437.80681    6.37843  68.639   <2e-16 ***
## nDate              1.67589    0.70250   2.386   0.0171 *  
## I(nDate * nDate)  -0.03272    0.01623  -2.016   0.0440 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 100.8 on 2458 degrees of freedom
## Multiple R-squared:  0.002914,	Adjusted R-squared:  0.002103 
## F-statistic: 3.592 on 2 and 2458 DF,  p-value: 0.02768

# linear + cubic (nDate^3)
  test3<-lm(TotalTimeInBed~poly(nDate,3),data=dailyInt)
  summary(test3)
## 
## Call:
## lm(formula = TotalTimeInBed ~ poly(nDate, 3), data = dailyInt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -369.85  -60.70   -0.17   60.92  425.13 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       453.95       2.03 223.676   <2e-16 ***
## poly(nDate, 3)1   178.04     100.68   1.768   0.0771 .  
## poly(nDate, 3)2  -203.11     100.68  -2.017   0.0438 *  
## poly(nDate, 3)3   230.78     100.68   2.292   0.0220 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 100.7 on 2457 degrees of freedom
## Multiple R-squared:  0.005042,	Adjusted R-squared:  0.003827 
## F-statistic:  4.15 on 3 and 2457 DF,  p-value: 0.006069

# compare AIC for the four models
  extractAIC(test)
## [1]     2.0 22709.4

  extractAIC(test2)
## [1]     3.00 22707.33

  extractAIC(test3)
## [1]     4.00 22704.08

(c) models, with random intercept per participant

  sleep<-lme4::lmer(TotalTimeInBed~poly(nDate,3)+(1|Id),data=dailyInt)

(d) generate predicted values

  dailyInt$fit_sleep<-fitted(sleep)

(e) rescale engagement and click data for plotting with Sleep

  dailyInt$click_sleep<-dailyInt$fit_click*
                               (mean(dailyInt$fit_sleep)/mean(dailyInt$fit_click))
  dailyInt$engage_sleep<-dailyInt$fit_engage*
                               (mean(dailyInt$fit_sleep)/mean(dailyInt$fit_engage))

(f) plot predicted values Sleep over time + predicted values of intervention clicks

Panel figures