Introduction to Causal Inference

Data Exercise

load Data

Code

#|label: source
source("https://raw.githubusercontent.com/go-bayes/templates/main/functions/funs.R")

Load Data

Code

#|label: load-data
#|eval: false
######### PART 1: DATA EXCERCISE ##############

# Create a folder called "data", in your Rstudio project. Download this file, add it to your the folder called "data" in your Rstudio project.
# "https://www.dropbox.com/s/vwqijg4ha17hbs1/nzavs_dat_synth_t10_t12?dl=0"



# This will read the synthetic data into Rstudio.  Note that the arrow package allows us to have lower memory demands in the storage and retrieval of data.
nzavs_synth <-
  arrow::read_parquet(here::here("data", "nzavs_dat_synth_t10_t12"))

Inspect

Code

## inspect colnames
colnames(nzavs_synth)

## inspect data properties
str(nzavs_synth)

Prepare data

Code

baseline_vars = c(
  "edu",
  "male",
  "eth_cat",
  "employed",
  "gen_cohort",
  "nz_dep2018",
  "nzsei13",
  "partner",
  "parent",
  "pol_orient",
  "rural_gch2018",
  "agreeableness",
  "conscientiousness",
  "extraversion",
  "honesty_humility",
  "openness",
  "neuroticism",
  "modesty",
  "religion_identification_level"
)


## Step 2, select the exposure variable.  This is the "cause"

exposure_var = c("perfectionism")


## step 3. select the outcome variable.  These are the outcomes.
outcome_vars_reflective = c("meaning_purpose",
                            "meaning_sense")


# optional: select exclusion variables (this will not be necessary most of the time)
exclude_vars = c("year_measured")


# the function "create_wide_data" should be in your environment. If not, make sure to run the first line of code in this script once more.  You may ignore the warnings.

prep_reflective <-
  create_wide_data(
    dat_long = nzavs_synth,
    #nzavs_synth,
    baseline_vars = baseline_vars,
    exposure_var = exposure_var,
    outcome_vars = outcome_vars_reflective
  )



# check. Note that any column that is the exposure or an outcome is added to "t0_".  This ensures the strongest possible confounding control, as described by VanderWeele:
# https://cdn1.sph.harvard.edu/wp-content/uploads/sites/603/2020/09/OutcomeWide_StatisticalScience.pdf

colnames(prep_reflective)

 [1] "t0_edu"                           "t0_male"                         
 [3] "t0_eth_cat"                       "t0_employed"                     
 [5] "t0_gen_cohort"                    "t0_nz_dep2018"                   
 [7] "t0_nzsei13"                       "t0_partner"                      
 [9] "t0_parent"                        "t0_pol_orient"                   
[11] "t0_rural_gch2018"                 "t0_agreeableness"                
[13] "t0_conscientiousness"             "t0_extraversion"                 
[15] "t0_honesty_humility"              "t0_openness"                     
[17] "t0_neuroticism"                   "t0_modesty"                      
[19] "t0_religion_identification_level" "t0_perfectionism"                
[21] "t0_meaning_purpose"               "t0_meaning_sense"                
[23] "t1_perfectionism"                 "t2_meaning_purpose"              
[25] "t2_meaning_sense"                

Code

# if the data is not working, you much run the code below to make the object in an object of the class dataframe.
# prep_reflective <- as.data.frame(prep_reflective)

create composite scores for constructs

Code

library(tidyverse) # should be loaded
 dt_ref <- prep_reflective |>
  mutate(id = factor(1:nrow(prep_reflective))) |>
  mutate(t1_perfectionism = round(t1_perfectionism)) |> # we create a three-level exposure to enable clear causal contrasts. We could also use a continous variable.
  mutate(
    t1_perfectionism_coarsen = cut(
      t1_perfectionism,
      breaks = c(1, 4, 5, 7),
      include.lowest = TRUE,
      include.highest = TRUE,
      na.rm = TRUE,
      right = FALSE
    )
  ) |>
  mutate(
    t0_eth_cat = as.factor(t0_eth_cat),
    t0_rural_gch2018 = as.factor(t0_rural_gch2018),
    t0_gen_cohort = as.factor(t0_gen_cohort)
  ) |>
  group_by(id) |>
  dplyr::mutate(t2_meaning = mean(c(t2_meaning_purpose,
                                    t2_meaning_sense),
                                  na.rm = TRUE)) |>
  ungroup() |>
  # transform numeric variables into z scores (improves estimation)
  dplyr::mutate(across(where(is.numeric), ~ scale(.x), .names = "{col}_z")) %>%
  # select only factors and numeric values that are z-scores
  select(id,
         where(is.factor),
         t1_perfectionism, # for comparison
         ends_with("_z"), ) |>
  # tidy data frame so that the columns are ordered by time (useful for more complex models)
  relocate(id, .before = starts_with("t1_"))   |>
  relocate(starts_with("t0_"), .before = starts_with("t1_"))  |>
  relocate(starts_with("t2_"), .after = starts_with("t1_"))


# inspect
levels(dt_ref$t1_perfectionism_coarsen)

[1] "[1,4)" "[4,5)" "[5,7]"

Code

# rename levels
dt_ref$t1_perfectionism_coarsen <-
  factor(
    dt_ref$t1_perfectionism_coarsen,
    levels = c("[1,4)", "[4,5)", "[5,7]"),
    labels = c("low", "medium", "high"),
    ordered = TRUE
  )

save your dataframe for future use

Code

#|eval: false
# make dataframe
dt_ref = as.data.frame(dt_ref)

# save data
saveRDS(dt_ref, here::here("data", "dt_ref"))

# read -- you may start here if you need to repeat the analysis

dt_ref <- readRDS(here::here("data", "dt_ref"))

prepare models

Code

dt_ref <- readRDS(here::here("data", "dt_ref"))

# needs to be data frame
dt_ref = data.frame(dt_ref)

# simplicity
df = dt_ref 

# this is the continuous exposure
X = "t1_perfectionism_z"

# this is a categorical exposure
X_pc <- "t1_perfectionism_coarsen"


# set our outcome variable:
Y = "t2_meaning_z" #note that we have created all numeric values into z-scores.  This will facilitate estimation and also interpretation. The outcome is expressed in standard deviation units


# Get baseline names
baseline_vars_reflective_cont = dt_ref |>
  dplyr::select(starts_with("t0")) |> colnames()

# See what we have created:  These are all the "t0_" variables.
# baseline_vars_reflective_cont


# to run these models our data need to be a dataframe (not a tibble or another kind of obect)
# above we've made the data a dataframe, but lets repeat in case you skipped that steip

dt_ref = as.data.frame(dt_ref)


# create our formula string, this time for the categorical variable.
formula_str_X <-
  paste(Y,
        "~",
        X ,
        "*",
        "(",
        paste(baseline_vars_reflective_cont, collapse = "+"),
        ")")
formula_str_X

[1] "t2_meaning_z ~ t1_perfectionism_z * ( t0_male+t0_eth_cat+t0_gen_cohort+t0_rural_gch2018+t0_edu_z+t0_employed_z+t0_nz_dep2018_z+t0_nzsei13_z+t0_partner_z+t0_parent_z+t0_pol_orient_z+t0_agreeableness_z+t0_conscientiousness_z+t0_extraversion_z+t0_honesty_humility_z+t0_openness_z+t0_neuroticism_z+t0_modesty_z+t0_religion_identification_level_z+t0_perfectionism_z+t0_meaning_purpose_z+t0_meaning_sense_z )"

Code

## regression based control


# fit model
m1 <- glm(as.formula(formula_str_X),
          # shortcut
          #  weights = weights, # will use weights with propensity score models
          family = "gaussian",
          data = df)

# we can look at the coefficients of this model, but again, it would be a mistake to interpret them
summary(m1)

Call:
glm(formula = as.formula(formula_str_X), family = "gaussian", 
    data = df)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.3374  -0.3647   0.0675   0.4199   3.2766  

Coefficients:
                                                                Estimate
(Intercept)                                                   -0.0458559
t1_perfectionism_z                                            -0.1347193
t0_maleNot_male                                                0.0632191
t0_eth_catmāori                                                0.0341978
t0_eth_catpacific                                             -0.0420690
t0_eth_catasian                                                0.0224974
t0_gen_cohort.L                                               -0.0203971
t0_gen_cohort.Q                                                0.0224781
t0_gen_cohort.C                                               -0.0005157
t0_gen_cohort^4                                               -0.0234273
t0_rural_gch2018medium_urban_accessibility                     0.0277126
t0_rural_gch2018low_urban_accessibility                        0.0196446
t0_rural_gch2018remote                                         0.0314218
t0_rural_gch2018very_remote                                    0.0184033
t0_edu_z                                                       0.0354573
t0_employed_z                                                  0.0104852
t0_nz_dep2018_z                                                0.0038250
t0_nzsei13_z                                                   0.0186043
t0_partner_z                                                   0.0186944
t0_parent_z                                                    0.0304512
t0_pol_orient_z                                                0.0268793
t0_agreeableness_z                                             0.0251108
t0_conscientiousness_z                                         0.0160022
t0_extraversion_z                                              0.0443726
t0_honesty_humility_z                                          0.0189023
t0_openness_z                                                  0.0116959
t0_neuroticism_z                                              -0.0440279
t0_modesty_z                                                   0.0008530
t0_religion_identification_level_z                             0.0601431
t0_perfectionism_z                                             0.0136652
t0_meaning_purpose_z                                           0.3689498
t0_meaning_sense_z                                             0.2410291
t1_perfectionism_z:t0_maleNot_male                             0.0331692
t1_perfectionism_z:t0_eth_catmāori                             0.0094140
t1_perfectionism_z:t0_eth_catpacific                          -0.0679774
t1_perfectionism_z:t0_eth_catasian                            -0.0852596
t1_perfectionism_z:t0_gen_cohort.L                            -0.0211112
t1_perfectionism_z:t0_gen_cohort.Q                             0.1133846
t1_perfectionism_z:t0_gen_cohort.C                            -0.0321318
t1_perfectionism_z:t0_gen_cohort^4                             0.0033751
t1_perfectionism_z:t0_rural_gch2018medium_urban_accessibility -0.0007409
t1_perfectionism_z:t0_rural_gch2018low_urban_accessibility    -0.0087372
t1_perfectionism_z:t0_rural_gch2018remote                     -0.0051989
t1_perfectionism_z:t0_rural_gch2018very_remote                 0.0406504
t1_perfectionism_z:t0_edu_z                                    0.0180683
t1_perfectionism_z:t0_employed_z                               0.0110596
t1_perfectionism_z:t0_nz_dep2018_z                            -0.0062207
t1_perfectionism_z:t0_nzsei13_z                               -0.0011272
t1_perfectionism_z:t0_partner_z                                0.0053248
t1_perfectionism_z:t0_parent_z                                 0.0111114
t1_perfectionism_z:t0_pol_orient_z                            -0.0003759
t1_perfectionism_z:t0_agreeableness_z                         -0.0052810
t1_perfectionism_z:t0_conscientiousness_z                     -0.0003144
t1_perfectionism_z:t0_extraversion_z                          -0.0041967
t1_perfectionism_z:t0_honesty_humility_z                       0.0026688
t1_perfectionism_z:t0_openness_z                               0.0086363
t1_perfectionism_z:t0_neuroticism_z                           -0.0145938
t1_perfectionism_z:t0_modesty_z                               -0.0026194
t1_perfectionism_z:t0_religion_identification_level_z          0.0086293
t1_perfectionism_z:t0_perfectionism_z                          0.0212526
t1_perfectionism_z:t0_meaning_purpose_z                        0.0231580
t1_perfectionism_z:t0_meaning_sense_z                         -0.0017437
                                                              Std. Error
(Intercept)                                                    0.0206239
t1_perfectionism_z                                             0.0217018
t0_maleNot_male                                                0.0158872
t0_eth_catmāori                                                0.0257156
t0_eth_catpacific                                              0.0513832
t0_eth_catasian                                                0.0401502
t0_gen_cohort.L                                                0.0537594
t0_gen_cohort.Q                                                0.0452441
t0_gen_cohort.C                                                0.0287586
t0_gen_cohort^4                                                0.0160948
t0_rural_gch2018medium_urban_accessibility                     0.0185188
t0_rural_gch2018low_urban_accessibility                        0.0226516
t0_rural_gch2018remote                                         0.0338997
t0_rural_gch2018very_remote                                    0.0697321
t0_edu_z                                                       0.0085782
t0_employed_z                                                  0.0073289
t0_nz_dep2018_z                                                0.0072973
t0_nzsei13_z                                                   0.0083108
t0_partner_z                                                   0.0075420
t0_parent_z                                                    0.0082115
t0_pol_orient_z                                                0.0079719
t0_agreeableness_z                                             0.0079531
t0_conscientiousness_z                                         0.0075374
t0_extraversion_z                                              0.0075663
t0_honesty_humility_z                                          0.0080126
t0_openness_z                                                  0.0076666
t0_neuroticism_z                                               0.0084511
t0_modesty_z                                                   0.0079318
t0_religion_identification_level_z                             0.0075053
t0_perfectionism_z                                             0.0106384
t0_meaning_purpose_z                                           0.0097171
t0_meaning_sense_z                                             0.0098484
t1_perfectionism_z:t0_maleNot_male                             0.0159842
t1_perfectionism_z:t0_eth_catmāori                             0.0248536
t1_perfectionism_z:t0_eth_catpacific                           0.0513900
t1_perfectionism_z:t0_eth_catasian                             0.0395309
t1_perfectionism_z:t0_gen_cohort.L                             0.0531681
t1_perfectionism_z:t0_gen_cohort.Q                             0.0443921
t1_perfectionism_z:t0_gen_cohort.C                             0.0280822
t1_perfectionism_z:t0_gen_cohort^4                             0.0158307
t1_perfectionism_z:t0_rural_gch2018medium_urban_accessibility  0.0181669
t1_perfectionism_z:t0_rural_gch2018low_urban_accessibility     0.0231386
t1_perfectionism_z:t0_rural_gch2018remote                      0.0363971
t1_perfectionism_z:t0_rural_gch2018very_remote                 0.0788117
t1_perfectionism_z:t0_edu_z                                    0.0086251
t1_perfectionism_z:t0_employed_z                               0.0070229
t1_perfectionism_z:t0_nz_dep2018_z                             0.0072208
t1_perfectionism_z:t0_nzsei13_z                                0.0082785
t1_perfectionism_z:t0_partner_z                                0.0072999
t1_perfectionism_z:t0_parent_z                                 0.0082109
t1_perfectionism_z:t0_pol_orient_z                             0.0078204
t1_perfectionism_z:t0_agreeableness_z                          0.0075244
t1_perfectionism_z:t0_conscientiousness_z                      0.0071301
t1_perfectionism_z:t0_extraversion_z                           0.0073804
t1_perfectionism_z:t0_honesty_humility_z                       0.0078333
t1_perfectionism_z:t0_openness_z                               0.0074053
t1_perfectionism_z:t0_neuroticism_z                            0.0082842
t1_perfectionism_z:t0_modesty_z                                0.0079651
t1_perfectionism_z:t0_religion_identification_level_z          0.0074253
t1_perfectionism_z:t0_perfectionism_z                          0.0081526
t1_perfectionism_z:t0_meaning_purpose_z                        0.0090046
t1_perfectionism_z:t0_meaning_sense_z                          0.0086903
                                                              t value Pr(>|t|)
(Intercept)                                                    -2.223  0.02621
t1_perfectionism_z                                             -6.208 5.59e-10
t0_maleNot_male                                                 3.979 6.96e-05
t0_eth_catmāori                                                 1.330  0.18360
t0_eth_catpacific                                              -0.819  0.41296
t0_eth_catasian                                                 0.560  0.57527
t0_gen_cohort.L                                                -0.379  0.70439
t0_gen_cohort.Q                                                 0.497  0.61933
t0_gen_cohort.C                                                -0.018  0.98569
t0_gen_cohort^4                                                -1.456  0.14554
t0_rural_gch2018medium_urban_accessibility                      1.496  0.13457
t0_rural_gch2018low_urban_accessibility                         0.867  0.38583
t0_rural_gch2018remote                                          0.927  0.35400
t0_rural_gch2018very_remote                                     0.264  0.79185
t0_edu_z                                                        4.133 3.60e-05
t0_employed_z                                                   1.431  0.15256
t0_nz_dep2018_z                                                 0.524  0.60018
t0_nzsei13_z                                                    2.239  0.02521
t0_partner_z                                                    2.479  0.01320
t0_parent_z                                                     3.708  0.00021
t0_pol_orient_z                                                 3.372  0.00075
t0_agreeableness_z                                              3.157  0.00160
t0_conscientiousness_z                                          2.123  0.03378
t0_extraversion_z                                               5.865 4.65e-09
t0_honesty_humility_z                                           2.359  0.01834
t0_openness_z                                                   1.526  0.12715
t0_neuroticism_z                                               -5.210 1.93e-07
t0_modesty_z                                                    0.108  0.91436
t0_religion_identification_level_z                              8.013 1.24e-15
t0_perfectionism_z                                              1.285  0.19899
t0_meaning_purpose_z                                           37.969  < 2e-16
t0_meaning_sense_z                                             24.474  < 2e-16
t1_perfectionism_z:t0_maleNot_male                              2.075  0.03800
t1_perfectionism_z:t0_eth_catmāori                              0.379  0.70486
t1_perfectionism_z:t0_eth_catpacific                           -1.323  0.18594
t1_perfectionism_z:t0_eth_catasian                             -2.157  0.03105
t1_perfectionism_z:t0_gen_cohort.L                             -0.397  0.69133
t1_perfectionism_z:t0_gen_cohort.Q                              2.554  0.01066
t1_perfectionism_z:t0_gen_cohort.C                             -1.144  0.25257
t1_perfectionism_z:t0_gen_cohort^4                              0.213  0.83117
t1_perfectionism_z:t0_rural_gch2018medium_urban_accessibility  -0.041  0.96747
t1_perfectionism_z:t0_rural_gch2018low_urban_accessibility     -0.378  0.70573
t1_perfectionism_z:t0_rural_gch2018remote                      -0.143  0.88642
t1_perfectionism_z:t0_rural_gch2018very_remote                  0.516  0.60601
t1_perfectionism_z:t0_edu_z                                     2.095  0.03621
t1_perfectionism_z:t0_employed_z                                1.575  0.11533
t1_perfectionism_z:t0_nz_dep2018_z                             -0.861  0.38899
t1_perfectionism_z:t0_nzsei13_z                                -0.136  0.89169
t1_perfectionism_z:t0_partner_z                                 0.729  0.46575
t1_perfectionism_z:t0_parent_z                                  1.353  0.17601
t1_perfectionism_z:t0_pol_orient_z                             -0.048  0.96167
t1_perfectionism_z:t0_agreeableness_z                          -0.702  0.48279
t1_perfectionism_z:t0_conscientiousness_z                      -0.044  0.96482
t1_perfectionism_z:t0_extraversion_z                           -0.569  0.56963
t1_perfectionism_z:t0_honesty_humility_z                        0.341  0.73334
t1_perfectionism_z:t0_openness_z                                1.166  0.24355
t1_perfectionism_z:t0_neuroticism_z                            -1.762  0.07816
t1_perfectionism_z:t0_modesty_z                                -0.329  0.74226
t1_perfectionism_z:t0_religion_identification_level_z           1.162  0.24520
t1_perfectionism_z:t0_perfectionism_z                           2.607  0.00915
t1_perfectionism_z:t0_meaning_purpose_z                         2.572  0.01013
t1_perfectionism_z:t0_meaning_sense_z                          -0.201  0.84098
                                                                 
(Intercept)                                                   *  
t1_perfectionism_z                                            ***
t0_maleNot_male                                               ***
t0_eth_catmāori                                                  
t0_eth_catpacific                                                
t0_eth_catasian                                                  
t0_gen_cohort.L                                                  
t0_gen_cohort.Q                                                  
t0_gen_cohort.C                                                  
t0_gen_cohort^4                                                  
t0_rural_gch2018medium_urban_accessibility                       
t0_rural_gch2018low_urban_accessibility                          
t0_rural_gch2018remote                                           
t0_rural_gch2018very_remote                                      
t0_edu_z                                                      ***
t0_employed_z                                                    
t0_nz_dep2018_z                                                  
t0_nzsei13_z                                                  *  
t0_partner_z                                                  *  
t0_parent_z                                                   ***
t0_pol_orient_z                                               ***
t0_agreeableness_z                                            ** 
t0_conscientiousness_z                                        *  
t0_extraversion_z                                             ***
t0_honesty_humility_z                                         *  
t0_openness_z                                                    
t0_neuroticism_z                                              ***
t0_modesty_z                                                     
t0_religion_identification_level_z                            ***
t0_perfectionism_z                                               
t0_meaning_purpose_z                                          ***
t0_meaning_sense_z                                            ***
t1_perfectionism_z:t0_maleNot_male                            *  
t1_perfectionism_z:t0_eth_catmāori                               
t1_perfectionism_z:t0_eth_catpacific                             
t1_perfectionism_z:t0_eth_catasian                            *  
t1_perfectionism_z:t0_gen_cohort.L                               
t1_perfectionism_z:t0_gen_cohort.Q                            *  
t1_perfectionism_z:t0_gen_cohort.C                               
t1_perfectionism_z:t0_gen_cohort^4                               
t1_perfectionism_z:t0_rural_gch2018medium_urban_accessibility    
t1_perfectionism_z:t0_rural_gch2018low_urban_accessibility       
t1_perfectionism_z:t0_rural_gch2018remote                        
t1_perfectionism_z:t0_rural_gch2018very_remote                   
t1_perfectionism_z:t0_edu_z                                   *  
t1_perfectionism_z:t0_employed_z                                 
t1_perfectionism_z:t0_nz_dep2018_z                               
t1_perfectionism_z:t0_nzsei13_z                                  
t1_perfectionism_z:t0_partner_z                                  
t1_perfectionism_z:t0_parent_z                                   
t1_perfectionism_z:t0_pol_orient_z                               
t1_perfectionism_z:t0_agreeableness_z                            
t1_perfectionism_z:t0_conscientiousness_z                        
t1_perfectionism_z:t0_extraversion_z                             
t1_perfectionism_z:t0_honesty_humility_z                         
t1_perfectionism_z:t0_openness_z                                 
t1_perfectionism_z:t0_neuroticism_z                           .  
t1_perfectionism_z:t0_modesty_z                                  
t1_perfectionism_z:t0_religion_identification_level_z            
t1_perfectionism_z:t0_perfectionism_z                         ** 
t1_perfectionism_z:t0_meaning_purpose_z                       *  
t1_perfectionism_z:t0_meaning_sense_z                            
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 0.479121)

    Null deviance: 9999.0  on 9999  degrees of freedom
Residual deviance: 4761.5  on 9938  degrees of freedom
AIC: 21085

Number of Fisher Scoring iterations: 2

simulate coefficients for the continuous exposure

Code

library(clarify)
nsims = 200
sim_model_r <- sim(m1, n = nsims)


# set to number of cores on your machine, e.g.
cores = 2

# simulate effect as modified
sim_estimand_r <- sim_ame(sim_model_r,
                          var = X,
                          cl = cores,
                          verbose = FALSE)


# this is the difference in expectations between everyone in the population being subject to a one standard deviation increase in perfectionism
# and everyone being subject to an average level of perfectionism.


# Estimate  2.5 % 97.5 %
#   dY/d(t1_perfectionism_z)   -0.160 -0.178 -0.140

summary(sim_estimand_r)

                         Estimate  2.5 % 97.5 %
dY/d(t1_perfectionism_z)   -0.160 -0.182 -0.142

Coarsened variable.

Code

# create our formula string:
formula_str_X_pc <-
  paste(Y,
        "~",
        X_pc ,
        "*",
        "(",
        paste(baseline_vars_reflective_cont, collapse = "+"),
        ")")

formula_str_X_pc

[1] "t2_meaning_z ~ t1_perfectionism_coarsen * ( t0_male+t0_eth_cat+t0_gen_cohort+t0_rural_gch2018+t0_edu_z+t0_employed_z+t0_nz_dep2018_z+t0_nzsei13_z+t0_partner_z+t0_parent_z+t0_pol_orient_z+t0_agreeableness_z+t0_conscientiousness_z+t0_extraversion_z+t0_honesty_humility_z+t0_openness_z+t0_neuroticism_z+t0_modesty_z+t0_religion_identification_level_z+t0_perfectionism_z+t0_meaning_purpose_z+t0_meaning_sense_z )"

Code

# fit model
m2 <- glm(as.formula(formula_str_X_pc),
          # shortcut
          #  weights = weights, # will use weights with propensity score models
          family = "gaussian",
          data = df)

# we can look at the coefficients of this model, but again it would be a mistake to interpret them

summary(m2)

Call:
glm(formula = as.formula(formula_str_X_pc), family = "gaussian", 
    data = df)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.1848  -0.3670   0.0660   0.4251   3.2601  

Coefficients:
                                                                        Estimate
(Intercept)                                                           -0.1226132
t1_perfectionism_coarsen.L                                            -0.1470404
t1_perfectionism_coarsen.Q                                             0.0968493
t0_maleNot_male                                                        0.0953799
t0_eth_catmāori                                                        0.0330656
t0_eth_catpacific                                                     -0.0797194
t0_eth_catasian                                                       -0.0450017
t0_gen_cohort.L                                                       -0.0638088
t0_gen_cohort.Q                                                        0.0783060
t0_gen_cohort.C                                                       -0.0171482
t0_gen_cohort^4                                                       -0.0209400
t0_rural_gch2018medium_urban_accessibility                             0.0356611
t0_rural_gch2018low_urban_accessibility                                0.0112271
t0_rural_gch2018remote                                                 0.0206451
t0_rural_gch2018very_remote                                            0.0708426
t0_edu_z                                                               0.0436332
t0_employed_z                                                          0.0170529
t0_nz_dep2018_z                                                       -0.0018689
t0_nzsei13_z                                                           0.0204286
t0_partner_z                                                           0.0165503
t0_parent_z                                                            0.0377576
t0_pol_orient_z                                                        0.0228034
t0_agreeableness_z                                                     0.0180559
t0_conscientiousness_z                                                 0.0192677
t0_extraversion_z                                                      0.0450764
t0_honesty_humility_z                                                  0.0222787
t0_openness_z                                                          0.0159350
t0_neuroticism_z                                                      -0.0602859
t0_modesty_z                                                          -0.0035097
t0_religion_identification_level_z                                     0.0604881
t0_perfectionism_z                                                     0.0008418
t0_meaning_purpose_z                                                   0.3868685
t0_meaning_sense_z                                                     0.2434801
t1_perfectionism_coarsen.L:t0_maleNot_male                             0.0620947
t1_perfectionism_coarsen.Q:t0_maleNot_male                            -0.0431561
t1_perfectionism_coarsen.L:t0_eth_catmāori                             0.0669463
t1_perfectionism_coarsen.Q:t0_eth_catmāori                             0.1235800
t1_perfectionism_coarsen.L:t0_eth_catpacific                          -0.0718211
t1_perfectionism_coarsen.Q:t0_eth_catpacific                           0.0856952
t1_perfectionism_coarsen.L:t0_eth_catasian                            -0.1551102
t1_perfectionism_coarsen.Q:t0_eth_catasian                             0.0883442
t1_perfectionism_coarsen.L:t0_gen_cohort.L                            -0.0306497
t1_perfectionism_coarsen.Q:t0_gen_cohort.L                             0.1516702
t1_perfectionism_coarsen.L:t0_gen_cohort.Q                             0.1958547
t1_perfectionism_coarsen.Q:t0_gen_cohort.Q                             0.0454657
t1_perfectionism_coarsen.L:t0_gen_cohort.C                            -0.0322455
t1_perfectionism_coarsen.Q:t0_gen_cohort.C                             0.0440922
t1_perfectionism_coarsen.L:t0_gen_cohort^4                             0.0173854
t1_perfectionism_coarsen.Q:t0_gen_cohort^4                             0.0131898
t1_perfectionism_coarsen.L:t0_rural_gch2018medium_urban_accessibility  0.0090066
t1_perfectionism_coarsen.Q:t0_rural_gch2018medium_urban_accessibility  0.0005206
t1_perfectionism_coarsen.L:t0_rural_gch2018low_urban_accessibility    -0.0464747
t1_perfectionism_coarsen.Q:t0_rural_gch2018low_urban_accessibility    -0.0419324
t1_perfectionism_coarsen.L:t0_rural_gch2018remote                     -0.0830230
t1_perfectionism_coarsen.Q:t0_rural_gch2018remote                     -0.1385026
t1_perfectionism_coarsen.L:t0_rural_gch2018very_remote                 0.0971420
t1_perfectionism_coarsen.Q:t0_rural_gch2018very_remote                -0.0499774
t1_perfectionism_coarsen.L:t0_edu_z                                    0.0286493
t1_perfectionism_coarsen.Q:t0_edu_z                                   -0.0028539
t1_perfectionism_coarsen.L:t0_employed_z                               0.0252432
t1_perfectionism_coarsen.Q:t0_employed_z                               0.0091128
t1_perfectionism_coarsen.L:t0_nz_dep2018_z                            -0.0093324
t1_perfectionism_coarsen.Q:t0_nz_dep2018_z                             0.0005713
t1_perfectionism_coarsen.L:t0_nzsei13_z                                0.0009809
t1_perfectionism_coarsen.Q:t0_nzsei13_z                                0.0032192
t1_perfectionism_coarsen.L:t0_partner_z                                0.0012847
t1_perfectionism_coarsen.Q:t0_partner_z                                0.0115548
t1_perfectionism_coarsen.L:t0_parent_z                                 0.0270801
t1_perfectionism_coarsen.Q:t0_parent_z                                 0.0090702
t1_perfectionism_coarsen.L:t0_pol_orient_z                            -0.0006814
t1_perfectionism_coarsen.Q:t0_pol_orient_z                             0.0172947
t1_perfectionism_coarsen.L:t0_agreeableness_z                         -0.0189019
t1_perfectionism_coarsen.Q:t0_agreeableness_z                          0.0024354
t1_perfectionism_coarsen.L:t0_conscientiousness_z                     -0.0126309
t1_perfectionism_coarsen.Q:t0_conscientiousness_z                     -0.0194902
t1_perfectionism_coarsen.L:t0_extraversion_z                          -0.0002204
t1_perfectionism_coarsen.Q:t0_extraversion_z                           0.0165607
t1_perfectionism_coarsen.L:t0_honesty_humility_z                      -0.0027931
t1_perfectionism_coarsen.Q:t0_honesty_humility_z                      -0.0140992
t1_perfectionism_coarsen.L:t0_openness_z                               0.0065241
t1_perfectionism_coarsen.Q:t0_openness_z                              -0.0126349
t1_perfectionism_coarsen.L:t0_neuroticism_z                           -0.0234255
t1_perfectionism_coarsen.Q:t0_neuroticism_z                            0.0062206
t1_perfectionism_coarsen.L:t0_modesty_z                               -0.0108579
t1_perfectionism_coarsen.Q:t0_modesty_z                                0.0147372
t1_perfectionism_coarsen.L:t0_religion_identification_level_z          0.0227283
t1_perfectionism_coarsen.Q:t0_religion_identification_level_z          0.0279009
t1_perfectionism_coarsen.L:t0_perfectionism_z                          0.0320759
t1_perfectionism_coarsen.Q:t0_perfectionism_z                         -0.0455083
t1_perfectionism_coarsen.L:t0_meaning_purpose_z                        0.0411158
t1_perfectionism_coarsen.Q:t0_meaning_purpose_z                        0.0056432
t1_perfectionism_coarsen.L:t0_meaning_sense_z                         -0.0091829
t1_perfectionism_coarsen.Q:t0_meaning_sense_z                         -0.0111806
                                                                      Std. Error
(Intercept)                                                            0.0254701
t1_perfectionism_coarsen.L                                             0.0431872
t1_perfectionism_coarsen.Q                                             0.0450248
t0_maleNot_male                                                        0.0192675
t0_eth_catmāori                                                        0.0299149
t0_eth_catpacific                                                      0.0608525
t0_eth_catasian                                                        0.0426782
t0_gen_cohort.L                                                        0.0603945
t0_gen_cohort.Q                                                        0.0506044
t0_gen_cohort.C                                                        0.0321417
t0_gen_cohort^4                                                        0.0184486
t0_rural_gch2018medium_urban_accessibility                             0.0227806
t0_rural_gch2018low_urban_accessibility                                0.0280264
t0_rural_gch2018remote                                                 0.0427166
t0_rural_gch2018very_remote                                            0.0932044
t0_edu_z                                                               0.0105185
t0_employed_z                                                          0.0086131
t0_nz_dep2018_z                                                        0.0086805
t0_nzsei13_z                                                           0.0100606
t0_partner_z                                                           0.0085931
t0_parent_z                                                            0.0097982
t0_pol_orient_z                                                        0.0097893
t0_agreeableness_z                                                     0.0092234
t0_conscientiousness_z                                                 0.0085661
t0_extraversion_z                                                      0.0091048
t0_honesty_humility_z                                                  0.0096794
t0_openness_z                                                          0.0092394
t0_neuroticism_z                                                       0.0099422
t0_modesty_z                                                           0.0094387
t0_religion_identification_level_z                                     0.0092116
t0_perfectionism_z                                                     0.0113879
t0_meaning_purpose_z                                                   0.0105537
t0_meaning_sense_z                                                     0.0099679
t1_perfectionism_coarsen.L:t0_maleNot_male                             0.0314355
t1_perfectionism_coarsen.Q:t0_maleNot_male                             0.0352027
t1_perfectionism_coarsen.L:t0_eth_catmāori                             0.0484912
t1_perfectionism_coarsen.Q:t0_eth_catmāori                             0.0549365
t1_perfectionism_coarsen.L:t0_eth_catpacific                           0.1061646
t1_perfectionism_coarsen.Q:t0_eth_catpacific                           0.1046290
t1_perfectionism_coarsen.L:t0_eth_catasian                             0.0698406
t1_perfectionism_coarsen.Q:t0_eth_catasian                             0.0777872
t1_perfectionism_coarsen.L:t0_gen_cohort.L                             0.1029227
t1_perfectionism_coarsen.Q:t0_gen_cohort.L                             0.1062634
t1_perfectionism_coarsen.L:t0_gen_cohort.Q                             0.0861450
t1_perfectionism_coarsen.Q:t0_gen_cohort.Q                             0.0891283
t1_perfectionism_coarsen.L:t0_gen_cohort.C                             0.0545987
t1_perfectionism_coarsen.Q:t0_gen_cohort.C                             0.0567232
t1_perfectionism_coarsen.L:t0_gen_cohort^4                             0.0306661
t1_perfectionism_coarsen.Q:t0_gen_cohort^4                             0.0331920
t1_perfectionism_coarsen.L:t0_rural_gch2018medium_urban_accessibility  0.0367803
t1_perfectionism_coarsen.Q:t0_rural_gch2018medium_urban_accessibility  0.0419635
t1_perfectionism_coarsen.L:t0_rural_gch2018low_urban_accessibility     0.0461386
t1_perfectionism_coarsen.Q:t0_rural_gch2018low_urban_accessibility     0.0508341
t1_perfectionism_coarsen.L:t0_rural_gch2018remote                      0.0743191
t1_perfectionism_coarsen.Q:t0_rural_gch2018remote                      0.0736540
t1_perfectionism_coarsen.L:t0_rural_gch2018very_remote                 0.1618903
t1_perfectionism_coarsen.Q:t0_rural_gch2018very_remote                 0.1609781
t1_perfectionism_coarsen.L:t0_edu_z                                    0.0169322
t1_perfectionism_coarsen.Q:t0_edu_z                                    0.0194200
t1_perfectionism_coarsen.L:t0_employed_z                               0.0140222
t1_perfectionism_coarsen.Q:t0_employed_z                               0.0157635
t1_perfectionism_coarsen.L:t0_nz_dep2018_z                             0.0140633
t1_perfectionism_coarsen.Q:t0_nz_dep2018_z                             0.0159476
t1_perfectionism_coarsen.L:t0_nzsei13_z                                0.0163164
t1_perfectionism_coarsen.Q:t0_nzsei13_z                                0.0184681
t1_perfectionism_coarsen.L:t0_partner_z                                0.0140428
t1_perfectionism_coarsen.Q:t0_partner_z                                0.0156797
t1_perfectionism_coarsen.L:t0_parent_z                                 0.0160940
t1_perfectionism_coarsen.Q:t0_parent_z                                 0.0178048
t1_perfectionism_coarsen.L:t0_pol_orient_z                             0.0158645
t1_perfectionism_coarsen.Q:t0_pol_orient_z                             0.0179807
t1_perfectionism_coarsen.L:t0_agreeableness_z                          0.0144998
t1_perfectionism_coarsen.Q:t0_agreeableness_z                          0.0173259
t1_perfectionism_coarsen.L:t0_conscientiousness_z                      0.0135816
t1_perfectionism_coarsen.Q:t0_conscientiousness_z                      0.0159942
t1_perfectionism_coarsen.L:t0_extraversion_z                           0.0146683
t1_perfectionism_coarsen.Q:t0_extraversion_z                           0.0167994
t1_perfectionism_coarsen.L:t0_honesty_humility_z                       0.0155358
t1_perfectionism_coarsen.Q:t0_honesty_humility_z                       0.0179105
t1_perfectionism_coarsen.L:t0_openness_z                               0.0147235
t1_perfectionism_coarsen.Q:t0_openness_z                               0.0171878
t1_perfectionism_coarsen.L:t0_neuroticism_z                            0.0160470
t1_perfectionism_coarsen.Q:t0_neuroticism_z                            0.0183189
t1_perfectionism_coarsen.L:t0_modesty_z                                0.0153804
t1_perfectionism_coarsen.Q:t0_modesty_z                                0.0172620
t1_perfectionism_coarsen.L:t0_religion_identification_level_z          0.0149222
t1_perfectionism_coarsen.Q:t0_religion_identification_level_z          0.0169249
t1_perfectionism_coarsen.L:t0_perfectionism_z                          0.0178542
t1_perfectionism_coarsen.Q:t0_perfectionism_z                          0.0214321
t1_perfectionism_coarsen.L:t0_meaning_purpose_z                        0.0171386
t1_perfectionism_coarsen.Q:t0_meaning_purpose_z                        0.0193535
t1_perfectionism_coarsen.L:t0_meaning_sense_z                          0.0158506
t1_perfectionism_coarsen.Q:t0_meaning_sense_z                          0.0185719
                                                                      t value
(Intercept)                                                            -4.814
t1_perfectionism_coarsen.L                                             -3.405
t1_perfectionism_coarsen.Q                                              2.151
t0_maleNot_male                                                         4.950
t0_eth_catmāori                                                         1.105
t0_eth_catpacific                                                      -1.310
t0_eth_catasian                                                        -1.054
t0_gen_cohort.L                                                        -1.057
t0_gen_cohort.Q                                                         1.547
t0_gen_cohort.C                                                        -0.534
t0_gen_cohort^4                                                        -1.135
t0_rural_gch2018medium_urban_accessibility                              1.565
t0_rural_gch2018low_urban_accessibility                                 0.401
t0_rural_gch2018remote                                                  0.483
t0_rural_gch2018very_remote                                             0.760
t0_edu_z                                                                4.148
t0_employed_z                                                           1.980
t0_nz_dep2018_z                                                        -0.215
t0_nzsei13_z                                                            2.031
t0_partner_z                                                            1.926
t0_parent_z                                                             3.854
t0_pol_orient_z                                                         2.329
t0_agreeableness_z                                                      1.958
t0_conscientiousness_z                                                  2.249
t0_extraversion_z                                                       4.951
t0_honesty_humility_z                                                   2.302
t0_openness_z                                                           1.725
t0_neuroticism_z                                                       -6.064
t0_modesty_z                                                           -0.372
t0_religion_identification_level_z                                      6.566
t0_perfectionism_z                                                      0.074
t0_meaning_purpose_z                                                   36.657
t0_meaning_sense_z                                                     24.426
t1_perfectionism_coarsen.L:t0_maleNot_male                              1.975
t1_perfectionism_coarsen.Q:t0_maleNot_male                             -1.226
t1_perfectionism_coarsen.L:t0_eth_catmāori                              1.381
t1_perfectionism_coarsen.Q:t0_eth_catmāori                              2.250
t1_perfectionism_coarsen.L:t0_eth_catpacific                           -0.677
t1_perfectionism_coarsen.Q:t0_eth_catpacific                            0.819
t1_perfectionism_coarsen.L:t0_eth_catasian                             -2.221
t1_perfectionism_coarsen.Q:t0_eth_catasian                              1.136
t1_perfectionism_coarsen.L:t0_gen_cohort.L                             -0.298
t1_perfectionism_coarsen.Q:t0_gen_cohort.L                              1.427
t1_perfectionism_coarsen.L:t0_gen_cohort.Q                              2.274
t1_perfectionism_coarsen.Q:t0_gen_cohort.Q                              0.510
t1_perfectionism_coarsen.L:t0_gen_cohort.C                             -0.591
t1_perfectionism_coarsen.Q:t0_gen_cohort.C                              0.777
t1_perfectionism_coarsen.L:t0_gen_cohort^4                              0.567
t1_perfectionism_coarsen.Q:t0_gen_cohort^4                              0.397
t1_perfectionism_coarsen.L:t0_rural_gch2018medium_urban_accessibility   0.245
t1_perfectionism_coarsen.Q:t0_rural_gch2018medium_urban_accessibility   0.012
t1_perfectionism_coarsen.L:t0_rural_gch2018low_urban_accessibility     -1.007
t1_perfectionism_coarsen.Q:t0_rural_gch2018low_urban_accessibility     -0.825
t1_perfectionism_coarsen.L:t0_rural_gch2018remote                      -1.117
t1_perfectionism_coarsen.Q:t0_rural_gch2018remote                      -1.880
t1_perfectionism_coarsen.L:t0_rural_gch2018very_remote                  0.600
t1_perfectionism_coarsen.Q:t0_rural_gch2018very_remote                 -0.310
t1_perfectionism_coarsen.L:t0_edu_z                                     1.692
t1_perfectionism_coarsen.Q:t0_edu_z                                    -0.147
t1_perfectionism_coarsen.L:t0_employed_z                                1.800
t1_perfectionism_coarsen.Q:t0_employed_z                                0.578
t1_perfectionism_coarsen.L:t0_nz_dep2018_z                             -0.664
t1_perfectionism_coarsen.Q:t0_nz_dep2018_z                              0.036
t1_perfectionism_coarsen.L:t0_nzsei13_z                                 0.060
t1_perfectionism_coarsen.Q:t0_nzsei13_z                                 0.174
t1_perfectionism_coarsen.L:t0_partner_z                                 0.091
t1_perfectionism_coarsen.Q:t0_partner_z                                 0.737
t1_perfectionism_coarsen.L:t0_parent_z                                  1.683
t1_perfectionism_coarsen.Q:t0_parent_z                                  0.509
t1_perfectionism_coarsen.L:t0_pol_orient_z                             -0.043
t1_perfectionism_coarsen.Q:t0_pol_orient_z                              0.962
t1_perfectionism_coarsen.L:t0_agreeableness_z                          -1.304
t1_perfectionism_coarsen.Q:t0_agreeableness_z                           0.141
t1_perfectionism_coarsen.L:t0_conscientiousness_z                      -0.930
t1_perfectionism_coarsen.Q:t0_conscientiousness_z                      -1.219
t1_perfectionism_coarsen.L:t0_extraversion_z                           -0.015
t1_perfectionism_coarsen.Q:t0_extraversion_z                            0.986
t1_perfectionism_coarsen.L:t0_honesty_humility_z                       -0.180
t1_perfectionism_coarsen.Q:t0_honesty_humility_z                       -0.787
t1_perfectionism_coarsen.L:t0_openness_z                                0.443
t1_perfectionism_coarsen.Q:t0_openness_z                               -0.735
t1_perfectionism_coarsen.L:t0_neuroticism_z                            -1.460
t1_perfectionism_coarsen.Q:t0_neuroticism_z                             0.340
t1_perfectionism_coarsen.L:t0_modesty_z                                -0.706
t1_perfectionism_coarsen.Q:t0_modesty_z                                 0.854
t1_perfectionism_coarsen.L:t0_religion_identification_level_z           1.523
t1_perfectionism_coarsen.Q:t0_religion_identification_level_z           1.649
t1_perfectionism_coarsen.L:t0_perfectionism_z                           1.797
t1_perfectionism_coarsen.Q:t0_perfectionism_z                          -2.123
t1_perfectionism_coarsen.L:t0_meaning_purpose_z                         2.399
t1_perfectionism_coarsen.Q:t0_meaning_purpose_z                         0.292
t1_perfectionism_coarsen.L:t0_meaning_sense_z                          -0.579
t1_perfectionism_coarsen.Q:t0_meaning_sense_z                          -0.602
                                                                      Pr(>|t|)
(Intercept)                                                           1.50e-06
t1_perfectionism_coarsen.L                                            0.000665
t1_perfectionism_coarsen.Q                                            0.031498
t0_maleNot_male                                                       7.53e-07
t0_eth_catmāori                                                       0.269047
t0_eth_catpacific                                                     0.190212
t0_eth_catasian                                                       0.291706
t0_gen_cohort.L                                                       0.290751
t0_gen_cohort.Q                                                       0.121795
t0_gen_cohort.C                                                       0.593687
t0_gen_cohort^4                                                       0.256384
t0_rural_gch2018medium_urban_accessibility                            0.117517
t0_rural_gch2018low_urban_accessibility                               0.688730
t0_rural_gch2018remote                                                0.628891
t0_rural_gch2018very_remote                                           0.447226
t0_edu_z                                                              3.38e-05
t0_employed_z                                                         0.047744
t0_nz_dep2018_z                                                       0.829534
t0_nzsei13_z                                                          0.042327
t0_partner_z                                                          0.054135
t0_parent_z                                                           0.000117
t0_pol_orient_z                                                       0.019857
t0_agreeableness_z                                                    0.050304
t0_conscientiousness_z                                                0.024516
t0_extraversion_z                                                     7.51e-07
t0_honesty_humility_z                                                 0.021375
t0_openness_z                                                         0.084617
t0_neuroticism_z                                                      1.38e-09
t0_modesty_z                                                          0.710020
t0_religion_identification_level_z                                    5.41e-11
t0_perfectionism_z                                                    0.941074
t0_meaning_purpose_z                                                   < 2e-16
t0_meaning_sense_z                                                     < 2e-16
t1_perfectionism_coarsen.L:t0_maleNot_male                            0.048261
t1_perfectionism_coarsen.Q:t0_maleNot_male                            0.220253
t1_perfectionism_coarsen.L:t0_eth_catmāori                            0.167437
t1_perfectionism_coarsen.Q:t0_eth_catmāori                            0.024502
t1_perfectionism_coarsen.L:t0_eth_catpacific                          0.498734
t1_perfectionism_coarsen.Q:t0_eth_catpacific                          0.412784
t1_perfectionism_coarsen.L:t0_eth_catasian                            0.026379
t1_perfectionism_coarsen.Q:t0_eth_catasian                            0.256103
t1_perfectionism_coarsen.L:t0_gen_cohort.L                            0.765867
t1_perfectionism_coarsen.Q:t0_gen_cohort.L                            0.153524
t1_perfectionism_coarsen.L:t0_gen_cohort.Q                            0.023014
t1_perfectionism_coarsen.Q:t0_gen_cohort.Q                            0.609982
t1_perfectionism_coarsen.L:t0_gen_cohort.C                            0.554808
t1_perfectionism_coarsen.Q:t0_gen_cohort.C                            0.436987
t1_perfectionism_coarsen.L:t0_gen_cohort^4                            0.570776
t1_perfectionism_coarsen.Q:t0_gen_cohort^4                            0.691096
t1_perfectionism_coarsen.L:t0_rural_gch2018medium_urban_accessibility 0.806558
t1_perfectionism_coarsen.Q:t0_rural_gch2018medium_urban_accessibility 0.990102
t1_perfectionism_coarsen.L:t0_rural_gch2018low_urban_accessibility    0.313823
t1_perfectionism_coarsen.Q:t0_rural_gch2018low_urban_accessibility    0.409455
t1_perfectionism_coarsen.L:t0_rural_gch2018remote                     0.263972
t1_perfectionism_coarsen.Q:t0_rural_gch2018remote                     0.060076
t1_perfectionism_coarsen.L:t0_rural_gch2018very_remote                0.548488
t1_perfectionism_coarsen.Q:t0_rural_gch2018very_remote                0.756217
t1_perfectionism_coarsen.L:t0_edu_z                                   0.090678
t1_perfectionism_coarsen.Q:t0_edu_z                                   0.883169
t1_perfectionism_coarsen.L:t0_employed_z                              0.071854
t1_perfectionism_coarsen.Q:t0_employed_z                              0.563212
t1_perfectionism_coarsen.L:t0_nz_dep2018_z                            0.506962
t1_perfectionism_coarsen.Q:t0_nz_dep2018_z                            0.971423
t1_perfectionism_coarsen.L:t0_nzsei13_z                               0.952065
t1_perfectionism_coarsen.Q:t0_nzsei13_z                               0.861624
t1_perfectionism_coarsen.L:t0_partner_z                               0.927110
t1_perfectionism_coarsen.Q:t0_partner_z                               0.461182
t1_perfectionism_coarsen.L:t0_parent_z                                0.092480
t1_perfectionism_coarsen.Q:t0_parent_z                                0.610469
t1_perfectionism_coarsen.L:t0_pol_orient_z                            0.965741
t1_perfectionism_coarsen.Q:t0_pol_orient_z                            0.336148
t1_perfectionism_coarsen.L:t0_agreeableness_z                         0.192401
t1_perfectionism_coarsen.Q:t0_agreeableness_z                         0.888218
t1_perfectionism_coarsen.L:t0_conscientiousness_z                     0.352392
t1_perfectionism_coarsen.Q:t0_conscientiousness_z                     0.223033
t1_perfectionism_coarsen.L:t0_extraversion_z                          0.988010
t1_perfectionism_coarsen.Q:t0_extraversion_z                          0.324261
t1_perfectionism_coarsen.L:t0_honesty_humility_z                      0.857325
t1_perfectionism_coarsen.Q:t0_honesty_humility_z                      0.431181
t1_perfectionism_coarsen.L:t0_openness_z                              0.657697
t1_perfectionism_coarsen.Q:t0_openness_z                              0.462292
t1_perfectionism_coarsen.L:t0_neuroticism_z                           0.144377
t1_perfectionism_coarsen.Q:t0_neuroticism_z                           0.734185
t1_perfectionism_coarsen.L:t0_modesty_z                               0.480232
t1_perfectionism_coarsen.Q:t0_modesty_z                               0.393271
t1_perfectionism_coarsen.L:t0_religion_identification_level_z         0.127762
t1_perfectionism_coarsen.Q:t0_religion_identification_level_z         0.099281
t1_perfectionism_coarsen.L:t0_perfectionism_z                         0.072437
t1_perfectionism_coarsen.Q:t0_perfectionism_z                         0.033747
t1_perfectionism_coarsen.L:t0_meaning_purpose_z                       0.016457
t1_perfectionism_coarsen.Q:t0_meaning_purpose_z                       0.770611
t1_perfectionism_coarsen.L:t0_meaning_sense_z                         0.562371
t1_perfectionism_coarsen.Q:t0_meaning_sense_z                         0.547176
                                                                         
(Intercept)                                                           ***
t1_perfectionism_coarsen.L                                            ***
t1_perfectionism_coarsen.Q                                            *  
t0_maleNot_male                                                       ***
t0_eth_catmāori                                                          
t0_eth_catpacific                                                        
t0_eth_catasian                                                          
t0_gen_cohort.L                                                          
t0_gen_cohort.Q                                                          
t0_gen_cohort.C                                                          
t0_gen_cohort^4                                                          
t0_rural_gch2018medium_urban_accessibility                               
t0_rural_gch2018low_urban_accessibility                                  
t0_rural_gch2018remote                                                   
t0_rural_gch2018very_remote                                              
t0_edu_z                                                              ***
t0_employed_z                                                         *  
t0_nz_dep2018_z                                                          
t0_nzsei13_z                                                          *  
t0_partner_z                                                          .  
t0_parent_z                                                           ***
t0_pol_orient_z                                                       *  
t0_agreeableness_z                                                    .  
t0_conscientiousness_z                                                *  
t0_extraversion_z                                                     ***
t0_honesty_humility_z                                                 *  
t0_openness_z                                                         .  
t0_neuroticism_z                                                      ***
t0_modesty_z                                                             
t0_religion_identification_level_z                                    ***
t0_perfectionism_z                                                       
t0_meaning_purpose_z                                                  ***
t0_meaning_sense_z                                                    ***
t1_perfectionism_coarsen.L:t0_maleNot_male                            *  
t1_perfectionism_coarsen.Q:t0_maleNot_male                               
t1_perfectionism_coarsen.L:t0_eth_catmāori                               
t1_perfectionism_coarsen.Q:t0_eth_catmāori                            *  
t1_perfectionism_coarsen.L:t0_eth_catpacific                             
t1_perfectionism_coarsen.Q:t0_eth_catpacific                             
t1_perfectionism_coarsen.L:t0_eth_catasian                            *  
t1_perfectionism_coarsen.Q:t0_eth_catasian                               
t1_perfectionism_coarsen.L:t0_gen_cohort.L                               
t1_perfectionism_coarsen.Q:t0_gen_cohort.L                               
t1_perfectionism_coarsen.L:t0_gen_cohort.Q                            *  
t1_perfectionism_coarsen.Q:t0_gen_cohort.Q                               
t1_perfectionism_coarsen.L:t0_gen_cohort.C                               
t1_perfectionism_coarsen.Q:t0_gen_cohort.C                               
t1_perfectionism_coarsen.L:t0_gen_cohort^4                               
t1_perfectionism_coarsen.Q:t0_gen_cohort^4                               
t1_perfectionism_coarsen.L:t0_rural_gch2018medium_urban_accessibility    
t1_perfectionism_coarsen.Q:t0_rural_gch2018medium_urban_accessibility    
t1_perfectionism_coarsen.L:t0_rural_gch2018low_urban_accessibility       
t1_perfectionism_coarsen.Q:t0_rural_gch2018low_urban_accessibility       
t1_perfectionism_coarsen.L:t0_rural_gch2018remote                        
t1_perfectionism_coarsen.Q:t0_rural_gch2018remote                     .  
t1_perfectionism_coarsen.L:t0_rural_gch2018very_remote                   
t1_perfectionism_coarsen.Q:t0_rural_gch2018very_remote                   
t1_perfectionism_coarsen.L:t0_edu_z                                   .  
t1_perfectionism_coarsen.Q:t0_edu_z                                      
t1_perfectionism_coarsen.L:t0_employed_z                              .  
t1_perfectionism_coarsen.Q:t0_employed_z                                 
t1_perfectionism_coarsen.L:t0_nz_dep2018_z                               
t1_perfectionism_coarsen.Q:t0_nz_dep2018_z                               
t1_perfectionism_coarsen.L:t0_nzsei13_z                                  
t1_perfectionism_coarsen.Q:t0_nzsei13_z                                  
t1_perfectionism_coarsen.L:t0_partner_z                                  
t1_perfectionism_coarsen.Q:t0_partner_z                                  
t1_perfectionism_coarsen.L:t0_parent_z                                .  
t1_perfectionism_coarsen.Q:t0_parent_z                                   
t1_perfectionism_coarsen.L:t0_pol_orient_z                               
t1_perfectionism_coarsen.Q:t0_pol_orient_z                               
t1_perfectionism_coarsen.L:t0_agreeableness_z                            
t1_perfectionism_coarsen.Q:t0_agreeableness_z                            
t1_perfectionism_coarsen.L:t0_conscientiousness_z                        
t1_perfectionism_coarsen.Q:t0_conscientiousness_z                        
t1_perfectionism_coarsen.L:t0_extraversion_z                             
t1_perfectionism_coarsen.Q:t0_extraversion_z                             
t1_perfectionism_coarsen.L:t0_honesty_humility_z                         
t1_perfectionism_coarsen.Q:t0_honesty_humility_z                         
t1_perfectionism_coarsen.L:t0_openness_z                                 
t1_perfectionism_coarsen.Q:t0_openness_z                                 
t1_perfectionism_coarsen.L:t0_neuroticism_z                              
t1_perfectionism_coarsen.Q:t0_neuroticism_z                              
t1_perfectionism_coarsen.L:t0_modesty_z                                  
t1_perfectionism_coarsen.Q:t0_modesty_z                                  
t1_perfectionism_coarsen.L:t0_religion_identification_level_z            
t1_perfectionism_coarsen.Q:t0_religion_identification_level_z         .  
t1_perfectionism_coarsen.L:t0_perfectionism_z                         .  
t1_perfectionism_coarsen.Q:t0_perfectionism_z                         *  
t1_perfectionism_coarsen.L:t0_meaning_purpose_z                       *  
t1_perfectionism_coarsen.Q:t0_meaning_purpose_z                          
t1_perfectionism_coarsen.L:t0_meaning_sense_z                            
t1_perfectionism_coarsen.Q:t0_meaning_sense_z                            
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 0.4840355)

    Null deviance: 9999.0  on 9999  degrees of freedom
Residual deviance: 4795.3  on 9907  degrees of freedom
AIC: 21217

Number of Fisher Scoring iterations: 2

simulate coefficients

Code

library(clarify)
nsims = 200
sim_model_r2 <- sim(m2, n = nsims)


# set to number of cores on your machine, e.g.
cores = 4

# simulate effect as modified
sim_estimand_r2 <- sim_ame(sim_model_r2,
                           var = X_pc,
                           cl = cores,
                           verbose = FALSE)




summary(sim_estimand_r2)

             Estimate   2.5 %  97.5 %
E[Y(low)]      0.0747  0.0548  0.0916
E[Y(medium)]  -0.1220 -0.1617 -0.0849
E[Y(high)]    -0.1872 -0.2440 -0.1236

Suppose we want to contrast everyone being assigned to medium with everyone being assigned to high.

Code

sim_estimand_r2_focal <-
  transform(sim_estimand_r2, RD = `E[Y(low)]` - `E[Y(high)]`)


# RD describes the causal contrast on the risk difference scale.
summary(sim_estimand_r2_focal)

             Estimate   2.5 %  97.5 %
E[Y(low)]      0.0747  0.0548  0.0916
E[Y(medium)]  -0.1220 -0.1617 -0.0849
E[Y(high)]    -0.1872 -0.2440 -0.1236
RD             0.2619  0.1987  0.3161

Code

# The ATE for the effect of moving from low to high is .26 a standard deviation unit in meaning.  What this means is that the expected loss of meaning from perfectionism is about a quarter standard deviation


# > summary(sim_estimand_r2)
# Estimate   2.5 %  97.5 %
# E[Y(low)]      0.0747  0.0519  0.0950
# E[Y(medium)]  -0.1220 -0.1534 -0.0788
# E[Y(high)]    -0.1872 -0.2408 -0.1360


# We interpret these contrasts as the expected effects were everyone "low" verses everyone assigned "medium" versus everyone assigned "high"

CAUSAL GRAPHS

Code

# also load the ggdag package
if(!require(ggdag)){
  # Install the package if it is not already installed
  install.packages("ggdag")
}
# load the ggdag package
library(ggdag)

Problem 1: bilingualism on cognitive abilities

Code

## Using the DAG below as a starting point, create a DAG in R using the `ggdag` package that represents the causal relationships among bilingualism (B), cognitive abilities (C), and socioeconomic status (S).



dag1 <- dagify(C ~ B + S,
               B ~ S,
               coords = list(x = c(S = 1, B = 2, C = 3),
                             y = c(S = 1, B = 2, C = 1)),
               exposure = "B",
               outcome = "C")

# inspect
tidy_dagitty(dag1)

# A DAG with 3 nodes and 3 edges
#
# Exposure: B
# Outcome: C
#
# A tibble: 4 × 8
  name      x     y direction to     xend  yend circular
  <chr> <int> <int> <fct>     <chr> <int> <int> <lgl>   
1 B         2     2 ->        C         3     1 FALSE   
2 C         3     1 <NA>      <NA>     NA    NA FALSE   
3 S         1     1 ->        B         2     2 FALSE   
4 S         1     1 ->        C         3     1 FALSE   

Code

dag1_t <- tidy_dagitty(dag1)

# # plot
# ggdag(dag1_t)
# 
# # view
# ggdag::ggdag_paths(dag1_t)
# 
# # inspect
# ggdag_parents(dag1_t, "B")

# find adjustment set: adjusting for S is sufficient to control for confounding (on the model's assumptions)
ggdag_adjustment_set(dag1_t)