contextual effects in 3-level models

Dear Timothy,

This won't work as your averaged X's will be highly correlated with each
other and with the original X.

I often find it easier to reason on a mathematical model. How would you
translate your 'contextual' effects into an equation? Or at least
clarify what a 'contextual' effect is.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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Op do 9 sep. 2021 om 17:38 schreef Timothy MacKenzie <fswfswt at gmail.com>:

Dear Colleagues,

I'm revising my question for better clarity. Suppose we have two
nested grouping variables (ID1 and ID2). The data structure looks like
below.

To obtain the contextual effects for ID1 and ID2, I wonder which
option is appropriate?

#-- Option 1: Create mean of X across ID1 (X_ave_ID1) and mean of X
across ID2 *ignoring* ID1 (X_ave_ID2)
#-- Option 2: Create mean of X across ID1 (X_ave_ID1) and mean of X
across ID2    *within*  ID1 (X_ave_ID2)

For both options, then, I will fit (in lme4::lmer()):

y ~ X + X_ave_ID1 + X_ave_ID2 + (1 | ID1 / ID2)

Thank you,
Tim

#------ DATA  STRUCTURE AND R CODE:

ID1    ID2                   X                      y
1       1                       0.474111397    1.9534671
1       1                      -0.712228120   0.9355230
1       2                      -0.009957293   1.1088756
1       2                      -1.237918646   0.8675550
2       1                      -0.554944765   2.7831133
2       1                      -0.320668268   0.1479290
2       2                       1.066993108   0.1688187
2       2                     -1.084870417    1.0536264

library(dplyr)

#-- Option 1:
     data %>%
     group_by(ID1) %>%
     mutate(X_ave_ID1 = mean(X)) %>%
     group_by(ID2) %>%
     mutate(X_ave_ID2 = mean(X))

#-- Option 2:
   data %>%
   group_by(ID1) %>%
   mutate(X_ave_ID1 = mean(X)) %>%
   group_by(ID2, .add = TRUE) %>%
   mutate(X_ave_ID2 = mean(X))

On Mon, Sep 6, 2021 at 1:31 PM Timothy MacKenzie <fswfswt at gmail.com>
wrote:

Dear All,

Suppose X is a continuous predictor that can vary within and between
two nested grouping variables in a 3-level linear mixed model:

effect.size ~ X + (1 | studies/outcomes)

How can I obtain the within effect of X, contextual effect of X at
level 2, and contextual effect of X at level 3?

I can think of two options but wonder which one makes more sense
(below)?   For both options, I will fit:

effect.size ~ X + X_ave_study + X_ave_outcome + (1 | studies/outcomes)

Thank you,
Tim

library(dplyr)

#-- Option 1:
     data %>%
     group_by(study) %>%
     mutate(X_ave_study = mean(X)) %>%
     group_by(outcome) %>%                         ## Here mean of
outcome *ignoring* studies is computed
     mutate(X_ave_outcome = mean(X))

#-- Option 2:
   data %>%
   group_by(study) %>%
   mutate(X_ave_study = mean(X)) %>%
   group_by(outcome, .add = TRUE) %>%     ## Here mean of outcome
*within* each study is computed
   mutate(X_ave_outcome = mean(X))

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