Oh my bad! Thank you, James. Simon
On Sat, Dec 5, 2020 at 11:23 AM James Pustejovsky <jepusto at gmail.com> wrote:
Hi Simon, For a binary variable (as you've operationalized gender), the contextual effect is a comparison one category versus the reference level. If you repeated the analysis but using males as the reference level, I think you would find coefficients that are identical except of opposite sign. James On Wed, Dec 2, 2020 at 8:35 PM Simon Harmel <sim.harmel at gmail.com> wrote:
Hi James,
I keep coming back to our informative discussion in this thread. So a
quick follow-up. Last time, we did the following to obtain the contextual
effect for males. Given this model (i.e., mg_b_w), can we obtain the
contextual effect for females OR we need to fit a new model, this time with
males as the reference group?
Thank you, Simon
library(dplyr)
library(fastDummies)
library(lme4)
hsb <- read.csv("
https://raw.githubusercontent.com/rnorouzian/e/master/hsb.csv")
hsb2 <- hsb %>%
mutate(gender = ifelse(female==0,"M","F")) %>% # create
'gender' from variable ?female?
dummy_columns(select_columns = "gender") %>% # create dummies
for 'gender? (creates 2 but we need 1)
group_by(sch.id) %>% # group by
cluster id 'sch.id'
mutate(across(starts_with("gender_"), list(wthn = ~ . - mean(.), btw =
~ mean(.))))
mg_b_w <- lmer(math ~ gender_M_wthn + gender_M_btw + (1|sch.id), data =
hsb2)
fixef(mg_b_w)[["gender_M_btw"]] - fixef(mg_b_w)[["gender_M_wthn"]] #
gives 1.92 as the contextual effect for males
On Thu, Oct 29, 2020 at 2:09 PM James Pustejovsky <jepusto at gmail.com>
wrote:
My apologies! I had this backwards in my head. Revised explanation below:
With gender, if you include the group-mean-centered dummy variables and
the cluster-level means, then the contextual effect will be as you
described (gender_M_btw - gender_M_wthn). However, another approach would
be to leave the dummy variables uncentered. If you do it this way, then the
coefficient on gender_M_btw corresponds exactly to the contextual effect,
with no need to subtract out the coefficient on gender_M_wthn.
R code verifying the equivalence of these approaches:
library(dplyr)
library(fastDummies)
library(lme4)
hsb <- read.csv("
https://raw.githubusercontent.com/rnorouzian/e/master/hsb.csv")
hsb2 <- hsb %>%
mutate(gender = ifelse(female==0,"M","F")) %>% # create 'gender?
from variable ?female?
dummy_columns(select_columns = "gender") %>% # create dummies for
'gender? (creates 2 but we need 1)
group_by(sch.id) %>% # group by cluster
id 'sch.id'
mutate(across(starts_with("gender_"), list(wthn = ~ . - mean(.), btw =
~ mean(.))))
mg_b_w <- lmer(math ~ gender_M_wthn + gender_M_btw + (1|sch.id), data =
hsb2)
mg_b_d <- lmer(math ~ gender_M + gender_M_btw + (1|sch.id), data = hsb2)
fixef(mg_b_w)[["gender_M_btw"]] - fixef(mg_b_w)[["gender_M_wthn"]]
fixef(mg_b_d)[["gender_M_btw"]]
On Thu, Oct 29, 2020 at 1:57 PM Simon Harmel <sim.harmel at gmail.com>
wrote:
Thank you, James. For uniformity, I always (i.e., for both categorical
& numeric predictors) use the following method (using a dataset I found on
Stack Overflow).
So, in the case below, you're saying gender_M_btw is the contextual
effect itself?
Simon
library(dplyr)
library(fastDummies)
library(lme4)
hsb <- read.csv("
https://raw.githubusercontent.com/rnorouzian/e/master/hsb.csv")
hsb2 <- hsb %>%
mutate(gender = ifelse(female==0,"M","F")) %>% # create 'gender? from
variable ?female?
dummy_columns(select_columns = "gender") %>% # create dummies for
'gender? (creates 2 but we need 1)
group_by(sch.id) %>% # group by cluster id
'sch.id'
mutate(across(starts_with("gender_"), list(wthn = ~ . - mean(.), btw =
~ mean(.))))
mg_b_w <- lmer(math ~ gender_M_wthn + gender_M_btw + (1|sch.id), data
= hsb2)
On Thu, Oct 29, 2020 at 1:31 PM James Pustejovsky <jepusto at gmail.com>
wrote:
Hi Simon, There are different ways to parameterize contextual effects. With gender, if you include the regular dummy variables (without group-mean-centering) plus the cluster-level means, then the contextual effect will be as you described (gender_M_btw - gender_M_wthn). However, another approach would be to first group-mean-center the dummy variables. In this approach, for a male student, gender_M_wthn would be equal to 1 minus the proportion of male students in the cluster, and for a female student, gender_M_wthn would be equal to the negative of the proportion of male students in the cluster. If you do it this way, then the coefficient on gender_M_btw corresponds exactly to the contextual effect, with no need to subtract out the coefficient on gender_M_wthn. All that said, if you have more than two categories you will have more than one contextual effect. In your example, you have a contextual effect for M, which would be the average difference in the DV between two units who are both male, but belong to clusters that differ by 1 percentage point in the composition of males *and have the same proportion of other-gender students *(i.e., clusters that have 1 percentage point difference in males, and a -1 percentage point difference in females). And then you have a contextual effect for other, corresponding the average difference in the DV between two units who are both other-gender, but belong to clusters that differ by 1 percentage point in the composition of other *and have the same proportion of male-gender students *(i.e., clusters that have 1 percentage point difference in other, and a -1 percentage point difference in females). James On Thu, Oct 29, 2020 at 12:24 PM Simon Harmel <sim.harmel at gmail.com> wrote:
Dear James, This makes perfect sense, many thanks. However, one thing remains. I know the contextual effect coefficient is "b_btw - b_wthn". If we have two categories (as in the case of "gender") and take females as the reference category, then the contextual effect coefficient will be: gender_M_btw - gender_M_wthn But if we have more than two categories (say we add a third "gender" category called OTHER), then will the contextual effect coefficient be (sum of the betweens) - (sum of the withins)? (gender_M_btw + gender_OTHER_btw) - (gender_M_wthn + gender_OTHER_wthn) On Thu, Oct 29, 2020 at 9:44 AM James Pustejovsky <jepusto at gmail.com> wrote:
Hi Simon, With a binary or categorical predictor, one could operationalize the contextual effect in terms of proportions (0-1 scale) or percentages (0-100 scale). If proportions, like say proportion of vegetarians, then the contextual effect would be the average difference in the DV between two units who are both vegetarian (i.e., have the same value of the predictor), but belong to clusters that are all vegetarian versus all omnivorous (i.e., that differ by one unit in the proportion for that predictor). That will make the contextual effects look quite large because it's an extreme comparison--absurdly so, in this case, since there can't be a vegetarian in a cluster of all omnivores. If you operationalize the contextual effect in terms of percentages (e.g., % vegetarians) then you get the average difference in the DV between two units who are both vegetarian, but belong to clusters that differ by 1 percentage point in the proportion of vegetarians. All of this works for multi-category predictors also. Say that you had vegetarians, pescatarians, and omnivores, with omnivores as the reference category, then the model would include group-mean-centered dummy variables for vegetarians and pescatarians, plus group-mean predictors representing the proportion/percentage of vegetarians and proportion/percentage of pescatarians. You have to omit one category at each level to avoid collinearity with the intercept. James On Thu, Oct 29, 2020 at 1:32 AM Simon Harmel <sim.harmel at gmail.com> wrote:
Dear James, I'm returning to this after a while, a quick question. In your gender example, you used the term "%female" in your interpretation of the contextual effect. If the categorical predictor had more than 2 categories, then would you still use the term % in your interpretation? My understanding of contextual effect is below: Contextual effect is the average difference in the DV between two units (e.g., subjects) which have the same value on an IV (e.g., same gender), but belong to clusters (e.g., schools) whose mean/percentage on that IV differs by one unit (is unit percentage if IV is categorical?). Thank you, Simon On Sun, Jun 7, 2020 at 7:30 AM James Pustejovsky <jepusto at gmail.com> wrote:
Yes, it?s general and also applies outside the context of meta-analysis. See for example Raudenbush & Bryk (2002) for a good discussion on centering and contextual effects in hierarchical linear models. On Jun 6, 2020, at 11:07 PM, Simon Harmel <sim.harmel at gmail.com> wrote: Many thanks James. A quick follow-up. The strategy that you described is a general, regression modeling strategy, right? I mean even if we were fitting a multi-level model, the fixed-effects part of the formula had to include the same construction of (i.e., *b1 (% female-within)_ij + b2 (% female-between)_j*) in it? Thanks, Simon On Thu, Jun 4, 2020 at 9:42 AM James Pustejovsky < jepusto at gmail.com> wrote:
Hi Simon, Please keep the listserv cc'd so that others can benefit from these discussions. Unfortunately, I don't think there is any single answer to your question---analytic strategies just depend too much on what your research questions are and the substantive context that you're working in. But speaking generally, the advantages of splitting predictors into within- and between-study versions are two-fold. First is that doing this provides an understanding of the structure of the data you're working with, in that it forces one to consider *which* predictors have within-study variation and *how much *variation there is (e.g., perhaps many studies have looked at internalizing symptoms, many studies have looked at externalizing symptoms, but only a few have looked at both types of outcomes in the same sample). The second advantage is that within-study predictors have a distinct interpretation from between-study predictors, and the within-study version is often theoretically more interesting/salient. That's because comparisons of effect sizes based on within-study variation hold constant other aspects of the studies that could influence effect size (and that could muddy the interpretation of the moderator). Here is an example that comes up often in research synthesis projects. Suppose that you're interested in whether participant sex moderates the effect of some intervention. Most of the studies in the sample are of type A, such that only aggregated effect sizes can be calculated. For these type A studies, we are able to determine a) the average effect size across the full sample (pooling across sex) and b) the sex composition of the sample (e.g., % female). For a smaller number of studies of type B, we are able to obtain dis-aggregated results for subgroups of male and female participants. For these studies, we are able to determine a) the average effect size for males and b) the average effect size for females, plus c) the sex composition of each of the sub-samples (respectively 0% and 100% female). Without considering within/between variation in the predictor, a meta-regression testing for whether sex is a moderator is: Y_ij = b0 + b1 (% female)_ij + e_ij The coefficient b1 describes how effect size magnitude varies across samples that differ by 1% in the percent of females. But the estimate of this coefficient pools information across studies of type A and studies of type B, essentially assuming that the contextual effects (variance explained by sample composition) are the same as the individual-level moderator effects (how the intervention effect varies between males and females). Now, if we use the within/between decomposition, the meta-regression becomes: Y_ij = b0 + b1 (% female-within)_ij + b2 (% female-between)_j + e_ij In this model, b1 will be estimated *using only the studies of type B*, as an average of the moderator effects for the studies that provide dis-aggregated data. And b2 will be estimated using studies of type A and the study-level average % female in studies of type B. Thus b2 can be interpreted as a pure contextual effect (variance explained by sample composition). Why does this matter? It's because contextual effects usually have a much murkier interpretation than individual-level moderator effects. Maybe this particular intervention has been tested for several different professions (e.g., education, nursing, dentistry, construction), and professions that tend to have higher proportions of females are also those that tend to be lower-status. If there is a positive contextual effect for % female, then it might be that a) the intervention really is more effective for females than for males or b) the intervention is equally effective for males and females but tends to work better when used with lower-status professions. Looking at between/within study variance in the predictor lets us disentangle those possibilities, at least partially. James On Wed, Jun 3, 2020 at 9:27 AM Simon Harmel <sim.harmel at gmail.com> wrote:
Indeed that was the problem, Greta, Thanks. But James, in meta-analysis having multiple categorical variables each with several levels is very pervasive and they often vary both within and between studies. So, if for each level of each of such categorical variables we need to do this, this would certainly become a daunting task in addition to making the model extremely big. My follow-up question is what is your strategy after you create within and between dummies for each of such categorical variables? What are the next steps? Thank you very much, Simon p.s. After your `robu()` call I get: `Warning message: In sqrt(eigenval) : NaNs produced` On Wed, Jun 3, 2020 at 8:45 AM Gerta Ruecker < ruecker at imbi.uni-freiburg.de> wrote:
Simon Maybe there should not be a line break between "Relative and Rating"? For characters, for example if they are used as legends, line breaks sometimes matter. Best, Gerta Am 03.06.2020 um 15:32 schrieb James Pustejovsky:
I'm not sure what produced that error and I cannot reproduce
it. It may
have to do something with the version of dplyr. Here's an
alternative way
to recode the Scoring variable, which might be less prone to
versioning
differences:
library(dplyr)
library(fastDummies)
library(robumeta)
data("oswald2013")
oswald_centered <-
oswald2013 %>%
# make dummy variables
mutate(
Scoring = factor(Scoring,
levels = c("Absolute", "Difference
Score", "Relative
Rating"),
labels = c("Absolute", "Difference",
"Relative"))
) %>%
dummy_columns(select_columns = "Scoring") %>%
# centering by study
group_by(Study) %>%
mutate_at(vars(starts_with("Scoring_")),
list(wthn = ~ . - mean(.), btw = ~ mean(.))) %>%
# calculate Fisher Z and variance
mutate(
Z = atanh(R),
V = 1 / (N - 3)
)
# Use the predictors in a meta-regression model
# with Scoring = Absolute as the omitted category
robu(Z ~ Scoring_Difference_wthn + Scoring_Relative_wthn +
Scoring_Difference_btw + Scoring_Relative_btw,
data = oswald_centered, studynum = Study, var.eff.size
= V)
On Tue, Jun 2, 2020 at 10:20 PM Simon Harmel <
sim.harmel at gmail.com> wrote:
Many thanks, James! I keep getting the following error when
I run your
code: Error: unexpected symbol in: "Rating" = "Relative") oswald_centered" On Tue, Jun 2, 2020 at 10:00 PM James Pustejovsky <
jepusto at gmail.com>
wrote:
Hi Simon, The same strategy can be followed by using dummy variables
for each
unique level of a categorical moderator. The idea would be
to 1) create
dummy variables for each category, 2) calculate the
study-level means of
the dummy variables (between-cluster predictors), and 3)
calculate the
group-mean centered dummy variables (within-cluster
predictors). Just like
if you're working with regular categorical predictors,
you'll have to pick
one reference level to omit when using these sets of
predictors.
Here is an example of how to carry out such calculations in
R, using the
fastDummies package along with a bit of dplyr:
library(dplyr)
library(fastDummies)
library(robumeta)
data("oswald2013")
oswald_centered <-
oswald2013 %>%
# make dummy variables
mutate(
Scoring = recode(Scoring, "Difference Score" =
"Difference",
"Relative Rating" = "Relative")
) %>%
dummy_columns(select_columns = "Scoring") %>%
# centering by study
group_by(Study) %>%
mutate_at(vars(starts_with("Scoring_")),
list(wthn = ~ . - mean(.), btw = ~ mean(.)))
%>%
# calculate Fisher Z and variance
mutate(
Z = atanh(R),
V = 1 / (N - 3)
)
# Use the predictors in a meta-regression model
# with Scoring = Absolute as the omitted category
robu(Z ~ Scoring_Difference_wthn + Scoring_Relative_wthn +
Scoring_Difference_btw + Scoring_Relative_btw, data =
oswald_centered,
studynum = Study, var.eff.size = V) Kind Regards, James On Tue, Jun 2, 2020 at 6:49 PM Simon Harmel <
sim.harmel at gmail.com> wrote:
Hi All, Page 13 of *THIS ARTICLE <
*
(*top of the page*) recommends that if a *continuous
moderator *varies
both within and across studies in a meta-analysis, a
strategy is to break
that moderator down into two moderators by: *(a)* taking the mean of each study (between-cluster
effect),
*(b)* centering the predictor within each study
(within-cluster effect).
BUT what if my original moderator that varies both within
and across
studies is a *"categorical" *moderator? I appreciate an R demonstration of the strategy
recommended.
Thanks,
Simon
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-- Dr. rer. nat. Gerta R?cker, Dipl.-Math. Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center - University of Freiburg Stefan-Meier-Str. 26, D-79104 Freiburg, Germany Phone: +49/761/203-6673 Fax: +49/761/203-6680 Mail: ruecker at imbi.uni-freiburg.de Homepage: https://www.uniklinik-freiburg.de/imbi.html