[R-meta] "Categorical" moderator varying within and between studies
James Pustejovsky
jepu@to @end|ng |rom gm@||@com
Sat Dec 5 18:23:02 CET 2020
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 using 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 using 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 using 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 using 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 using 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 using 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 using 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 using 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 using 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 using 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 using 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 using 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 using 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 using 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 using gmail.com> wrote:
>>>>>>>>>>> >>>
>>>>>>>>>>> >>>> Hi All,
>>>>>>>>>>> >>>>
>>>>>>>>>>> >>>> Page 13 of *THIS ARTICLE
>>>>>>>>>>> >>>> <
>>>>>>>>>>> >>>>
>>>>>>>>>>> https://cran.r-project.org/web/packages/robumeta/vignettes/robumetaVignette.pdf
>>>>>>>>>>> >>>>> *
>>>>>>>>>>> >>>> (*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
>>>>>>>>>>> >>>>
>>>>>>>>>>> >>>> [[alternative HTML version deleted]]
>>>>>>>>>>> >>>>
>>>>>>>>>>> >>>> _______________________________________________
>>>>>>>>>>> >>>> R-sig-meta-analysis mailing list
>>>>>>>>>>> >>>> R-sig-meta-analysis using r-project.org
>>>>>>>>>>> >>>> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>>>>>>>>>>> >>>>
>>>>>>>>>>> > [[alternative HTML version deleted]]
>>>>>>>>>>> >
>>>>>>>>>>> > _______________________________________________
>>>>>>>>>>> > R-sig-meta-analysis mailing list
>>>>>>>>>>> > R-sig-meta-analysis using r-project.org
>>>>>>>>>>> > https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>>>>>>>>>>>
>>>>>>>>>>> --
>>>>>>>>>>>
>>>>>>>>>>> Dr. rer. nat. Gerta Rücker, 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 using imbi.uni-freiburg.de
>>>>>>>>>>> Homepage: https://www.uniklinik-freiburg.de/imbi.html
>>>>>>>>>>>
>>>>>>>>>>>
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