microgoal 1st round data

Let’s read in the data first

Hey folks I started writing this at the airport……so sorry for the delay I will see how much I can do,

I will assign some to-dos at the end of the document for Bingcheng to follow it up (sorry Bingcheng and thank you Bingcheng! Will bring food for you from China :D)

library(readxl)
library(tidyr)
library(tidyverse)

df <- read_xlsx('/Users/haochensong/Desktop/micro-goal data/Cleaned_Data.xlsx', skip = 2)

db <- df %>%  select(
  `Expectation Arm`,
  `Activity Arm`,
  `Benefit and Barrier Arm`,
  `Example Arm`,
  `Bigger Goal Arm`,
  Pre_Commitment,
  Post_Commitment
)

db$id <- 1:nrow(db)

Model Building, let’s see

turn into long format first:

db_long <- db %>%
  gather(key = "Time", value = "Commitment", Pre_Commitment, Post_Commitment) %>%
  mutate(Time = factor(ifelse(Time == "Pre_Commitment", "Pre", "Post")))

looks good, let’s fit the mixed effect model:

library(lme4)
model <- lmer(Commitment ~ Time * (`Expectation Arm` + `Activity Arm` + `Benefit and Barrier Arm` + `Example Arm` + `Bigger Goal Arm`) + (1 | id), data = db_long)

summary(model)

Linear mixed model fit by REML ['lmerMod']
Formula: 
Commitment ~ Time * (`Expectation Arm` + `Activity Arm` + `Benefit and Barrier Arm` +  
    `Example Arm` + `Bigger Goal Arm`) + (1 | id)
   Data: db_long

REML criterion at convergence: 1068.1

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-1.88709 -0.52336 -0.01723  0.44097  2.83113 

Random effects:
 Groups   Name        Variance Std.Dev.
 id       (Intercept) 4.500    2.121   
 Residual             4.932    2.221   
Number of obs: 220, groups:  id, 110

Fixed effects:
                                   Estimate Std. Error t value
(Intercept)                        10.93677    0.78334  13.962
TimePre                             0.72413    0.80108   0.904
`Expectation Arm`N                  0.59992    0.59763   1.004
`Activity Arm`m                     0.92340    0.72671   1.271
`Activity Arm`r                     1.04736    0.72111   1.452
`Benefit and Barrier Arm`o         -0.40193    0.60500  -0.664
`Example Arm`v                      0.33022    0.60013   0.550
`Bigger Goal Arm`o                  0.10406    0.59104   0.176
TimePre:`Expectation Arm`N          0.30415    0.61116   0.498
TimePre:`Activity Arm`m            -0.73854    0.74317  -0.994
TimePre:`Activity Arm`r            -0.09366    0.73745  -0.127
TimePre:`Benefit and Barrier Arm`o  0.41947    0.61871   0.678
TimePre:`Example Arm`v              0.73074    0.61372   1.191
TimePre:`Bigger Goal Arm`o          0.01531    0.60442   0.025

Correlation matrix not shown by default, as p = 14 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

also anova table:

anova_table <- anova(model)
print(anova_table)

Analysis of Variance Table
                               npar Sum Sq Mean Sq F value
Time                              1 78.005  78.005 15.8172
`Expectation Arm`                 1  8.110   8.110  1.6445
`Activity Arm`                    2 14.592   7.296  1.4794
`Benefit and Barrier Arm`         1  0.212   0.212  0.0429
`Example Arm`                     1  8.934   8.934  1.8116
`Bigger Goal Arm`                 1  0.239   0.239  0.0484
Time:`Expectation Arm`            1  0.400   0.400  0.0812
Time:`Activity Arm`               2  8.667   4.334  0.8788
Time:`Benefit and Barrier Arm`    1  3.479   3.479  0.7055
Time:`Example Arm`                1  6.989   6.989  1.4171
Time:`Bigger Goal Arm`            1  0.003   0.003  0.0006

ToDo for Bingcheng:

it looks like Benefit and Barrier Arm definitely is good, so is the interaction between Time and Bigger Goal Arm

I don’t have the time now to write out the summary as my plane is boarding in 5 minutes…

can you try out other models, and consult Ilya for more interpretation?

• we could decrease the number of interaction terms here?

• we could use this info to better fit our power analysis?

• this is quite good results, consult Ilya how we should report it?