[R-meta] "Categorical" moderator varying within and between studies

Simon Harmel @|m@h@rme| @end|ng |rom gm@||@com
Sat Dec 5 22:26:08 CET 2020 

Oh my bad! Thank you, James.

Simon

On Sat, Dec 5, 2020 at 11:23 AM James Pustejovsky <jepusto using 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 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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