README.Rmd

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# blsmeta: Bayesian Location-Scale Meta-Analysis

[![Build Status](https://www.travis-ci.com/donaldRwilliams/blsmeta.svg?branch=main)](https://travis-ci.com/donaldRwilliams/blsmeta)

The goal of **blsmeta** is to provide a user-friendly interface for
Bayesian meta-analysis, including fixed-effects, two-level, 
and three-level (for dependent effect sizes) 
random-effects models.

Additionally, a key feature of **blsmeta** is "scale" modeling, 
which allows for predicting the variance components with moderators 
(e.g., perhaps between-study variance is not constant across studies). 
As a result, heterogeneity statistics and prediction intervals are then a function of 
those same moderators, thereby opening the door to **better
understanding heterogeneity in meta-analysis**.


Version 1 is forthcoming, say, by the end of June 2021. 


You can install the development version from [GitHub](https://github.com/) with:

``` r
# install.packages("devtools")
devtools::install_github("donaldRwilliams/blsmeta")
```
Note that the development version will be fully usable, in so far 
as it will have been tested, documented, etc. It will gradually
include more functions over the coming weeks 
(merged from other branches), culminating in the official release.

Below, there are some simple examples demonstrating how to use **blsmeta**.
In the future, there will be several examples showcasing the utility
of scale modeling in meta-analysis.

## Table of Contents

-   [Installing JAGS](#installing-jags)
-   [Fixed-Effects Model](#fixed-effects-model)
      -   [Overall Effect](#overall-effect)
      -   [Moderator](#moderator)
-   [Two-Level Model](#two-level-model)
      -   [Overall Effect](#overall-effect-1)
      -   [Scale Moderator](#scale-moderator)
            -   [Predicted Values](#predicted-values)
-   [Three-Level Model](#three-level-model)
      -   [Comparing Variance Components](#comparing-variance-components)
-   [MCMC metafor](#mcmc-metafor)
-   [Custom Priors](#user-defined-priors)
-   [Student Led Projects](#forthcoming-features)
      -   [Diversity](#diversity)




## Installing JAGS
**blsmeta** uses the popular Bayesian software JAGS to estimate the models. 
It must be downloaded from the following link: [https://sourceforge.net/projects/mcmc-jags/files/](https://sourceforge.net/projects/mcmc-jags/files/)


## Packages
```
# install for data
if (!require('psymetadata')){
  install.packages('psymetadata')
  }
library(psymetadata)
library(blsmeta)
```

## Fixed-Effects Model
### Overall Effect
```
# fit model
fit_fe <- blsmeta(yi = yi, vi = vi, 
                  data = gnambs2020)
                  
# results
fit_fe

#> Model: Fixed-Effects
#> Studies: 67 
#> Samples: 20000 (4 chains)
#> Formula: ~ 1 
#> ------
#> Location:
#>             Post.mean Post.sd Cred.lb Cred.ub Rhat
#> (Intercept)     -0.07    0.03   -0.12   -0.02 1.00
#>
#> ------
#> Date: Mon Jun 07 12:03:56 2021 
```
There is an important difference from the **metafor** package, where, by default,
a random-effects model is fitted. This is not the case in **blsmeta**, where, by default, a fixed-effects model will be estimated if the level two variable is 
not provided.

### Moderator
```
fit_fe <- blsmeta(yi = yi, vi = vi, 
                  mods = ~ 0 + color,
                  data = gnambs2020)

# results
fit_fe

#> Model: Fixed-Effects
#> Studies: 67 
#> Samples: 20000 (4 chains)
#> Formula: ~ 0 + color 
#> ------
#> Location:
#>            Post.mean Post.sd Cred.lb Cred.ub Rhat
#> colorblack     -0.04    0.13   -0.30    0.22 1.00
#> colorblue      -0.04    0.07   -0.18    0.10 1.00
#> colorgray      -0.12    0.05   -0.22   -0.01 1.00
#> colorgreen     -0.06    0.03   -0.13    0.00 1.00
#> colorwhite      0.00    0.12   -0.23    0.22 1.00

#> ------
#> Date: Mon Jun 07 12:21:07 2021 
```
In the not too distant future (this was written on  6/7/21), it
will be possible to compare those effects (e.g., `colorgreen - colorwhite`).

## Two-Level Model
## Overall Effect
A two-level random-effects meta-analysis is implemented with

```
fit_re <- blsmeta(yi = yi, vi = vi, 
                  es_id = es_id,
                  data = gnambs2020)

# results
fit_re

#> Model: Two-Level
#> Studies: 67 
#> Samples: 20000 (4 chains)
#> Location Formula: ~ 1 
#> Scale Formula: ~ 1 
#> Note: 'Scale' on standard deviation scale
#> ------
#> Scale:
#>               Post.mean Post.sd Cred.lb Cred.ub Rhat
#> sd(Intercept)      0.10    0.06    0.02    0.22 1.00
#> 
#> Location:
#>             Post.mean Post.sd Cred.lb Cred.ub Rhat
#> (Intercept)     -0.08    0.03   -0.14   -0.02 1.00
#>
#> ------
#> Date: Mon Jun 07 12:26:24 2021 
```
Notice the argument `es_id`, which corresponds to the effect size id 
(`1:k`, where `k` is the number of studies).

## Scale Moderator
A key feature of **blsmeta** is scale modeling that allows for predicting 
the between-study variance (or "scale") with moderators 
(just like for the effect size or "location"). In this following example, 
heterogeneity is predicted study size.

```
fit_re <- blsmeta(yi = yi, vi = vi, 
                  es_id = es_id,
                  mods_scale2 = ~ n, 
                  data = gnambs2020)

# results
fit_re

#> Model: Two-Level
#> Studies: 67 
#> Samples: 20000 (4 chains)
#> Location Formula: ~ 1 
#> Scale Formula: ~ n 
#> Note: 'Scale' on standard deviation scale
#> ------
#> Scale:
#>             Post.mean Post.sd Cred.lb Cred.ub Rhat
#> (Intercept)      0.01    0.42   -0.77    0.88 1.03
#> n               -0.03    0.01   -0.05   -0.01 1.03
#>
#> Location:
#>             Post.mean Post.sd Cred.lb Cred.ub Rhat
#> (Intercept)     -0.06    0.03   -0.11    0.00 1.00
#>
#> ------
#> Date: Mon Jun 07 12:30:18 2021 
```
Notice that the `n` parameter is negative, implying that studies with larger 
sample sizes are more consistent (i.e., less heterogeneity). That effect
is on the log-scale, which is far from intuitive. 


### Predicted Values
To make sense of the scale model, it is possible to obtain predicted values of 
between-study heterogeneity at particular values of the moderator, that is,

```
tau2(fit_re, type = "sd", 
     newdata_scale2 = data.frame(n = seq(20, 200, 20)))

#>    Post.mean Post.sd Cred.lb Cred.ub
#> 1      0.634   0.165   0.357   1.003
#> 2      0.378   0.083   0.226   0.553
#> 3      0.234   0.072   0.096   0.372
#> 4      0.149   0.063   0.037   0.273
#> 5      0.098   0.053   0.014   0.207
#> 6      0.065   0.043   0.005   0.161
#> 7      0.045   0.035   0.002   0.126
#> 8      0.031   0.028   0.001   0.100
#> 9      0.022   0.022   0.000   0.080
#> 10     0.015   0.018   0.000   0.063
```
Notice `type = "sd"`, which ensures we are on the standard deviation scale 
(easier to interpret). The results indicate that there is quite a bit of
heterogeneity in small studies, but it goes to practically zero as 
study size increases.


## Three-Level Model
Three-level location-scale meta-analysis is fully implemented as well. The key is providing the `study_id` argument, which is the higher level grouping variable 
that the effect sizes are nested within. This accommodates dependent 
effect sizes.

```
fit <-  blsmeta(yi = yi, 
                vi = vi, 
                es_id = es_id,
                study_id = study_id,
                data = gnambs2020)
              
fit

#> Model: Three-Level
#> Studies2: 67 
#> Studies3: 22 
#> Samples: 20000 (4 chains)
#> Location Formula: ~ 1 
#> Scale2 Formula: ~ 1 
#> Scale3 Formula: ~ 1 
#> Note: 'Scale' on standard deviation scale
#> ------
#> Scale2:
#>               Post.mean Post.sd Cred.lb Cred.ub Rhat
#> sd(Intercept)      0.06    0.04    0.01    0.15 1.00
#> 
#> Scale3:
#>               Post.mean Post.sd Cred.lb Cred.ub Rhat
#> sd(Intercept)      0.20    0.06    0.09    0.34 1.01
#> 
#> Location:
#>             Post.mean Post.sd Cred.lb Cred.ub Rhat
#> (Intercept)     -0.12    0.06   -0.25   -0.02 1.00
#> 
#> ------
#> Date: Sun Jun 13 11:27:08 2021 
```

### Comparing Variance Components
One question might be whether one variance component is larger, which 
can be tested with the `linear_hypothesis` function.

```
linear_hypothesis(obj = fit, 
                  cred = 0.90,
                  lin_comb = "scale3_Intercept > scale2_Intercept",
                  sub_model = "scale")
                  
#> Hypotheses:
#>  C1: scale3_Intercept > scale2_Intercept 
#> ------ 
#> Posterior Summary:
#> 
#>    Post.mean Post.sd Cred.lb Cred.ub Pr.less Pr.greater
#> C1      1.27    0.73    0.14    2.51    0.03       0.97
#> ------ 
#> Note:
#> Pr.less: Posterior probability less than zero
#> Pr.greater: Posterior probability greater than zero
```
These estimates are on the log-scale, and there is a 0.97 posterior 
probability that the level three variance component is larger
than the level two variance component. 

In the future, it will be possible to compare these models with the Bayes factor.

## MCMC metafor
The package **metafor** is perhaps the gold-standard for 
meta-analysis in `R`. In **blsmeta**, it is possible to sample from the 
posterior distribution of a model originally estimated with **metafor** 
(`rma` objects are currently supported).

```
library(metafor)

fit <- mcmc_rma(rma(yi = yi, vi = vi, 
                 method = "FE", data = gnambs2020), 
                 data = gnambs2020)
# results
fit

#> Model: Fixed-Effects
#> Studies: 67 
#> Samples: 20000 (4 chains)
#> Formula: ~ 1 
#> ------
#> Location:
#>             Post.mean Post.sd Cred.lb Cred.ub Rhat
#> (Intercept)     -0.07    0.03   -0.12   -0.02 1.00
#>
#> ------
#> Date: Mon Jun 07 13:27:13 2021 
```
This function works for any kind of model fitted with `rma`.


## User-Defined Priors

User-defined priors can be defined for each parameter. This is accomplished
with the `assign_prior` function. For example, 

```
prior <- 
  c(assign_prior(param = "(Intercept)", 
                prior = "dnorm(0, pow(1, -2))", 
                dpar = "location"),
    assign_prior(param = "n", 
                 prior = "dnorm(0, 1)", 
                 dpar = "location"),
    assign_prior(param = "(Intercept)", 
              prior = "dnorm(-0.5, pow(1.5, -2))", 
              dpar = "scale", level = "two")
    )
```
The `pow(1.5, -2)` allows for specifying the standard deviation, 
whereas `JAGS` uses the precision, or the inverse of the variance, which
can be confusing (hence use `pow(., -2)`). This would then be used 
in the `prior` argument of `blsmeta`.


For a sanity check, it is possible to verify that the priors made it to the correct parameters as follows


```
priors <- make_prior(yi = yi, 
           vi = vi, 
           mods = ~ n,
           prior = prior,
           es_id = es_id,
           study_id = study_id,
           data = gnambs2020)

priors

#> #location priors
#> 
#> #(Intercept)
#> beta[1] ~ dnorm(0, pow(1, -2))
#> 
#> #n
#> beta[2] ~ dnorm(0, 1)
#> 
#> #scale level two priors
#> 
#> #(Intercept)
#> gamma[1] ~ dnorm(-0.5, pow(1.5, -2))
#> 
#> #scale level three priors
#> #Intercept
#> eta[1] ~ dnorm(-2, 1)
```

Notice that the  "scale" priors are negative. At first, this may not seem
correct because the scale refers to the variance. By default, however,
a log-linear model is fitted to the variance components. As a result,
the priors are on the log-scale which is very flexible on the one hand, but
on the other, not very intuitive. 

To better understand those priors,
use `sample_prior`.

```
samps <- sample_prior(priors, iter = 50000)
```

Then you can plot the prior with `hist(exp(samps$gamma), xlim = c(0, 2), breaks = 10000)`.

## Forthcoming Features
There are a variety of things strategically left out of **blsmeta**. This
is because I am hoping to be a professor. To this end, I am planning 
to tackle the following with students that join my lab:

1. Bayesian hypothesis testing (with the Bayes factor)

2. Visualization (with **ggplot2**)

3. Shiny Application

4. Website


Option 1 could be a first year project for a graduate student. 
I have several other ideas for meta-analysis (to help get the ball rolling, 
if interested), but these would not likely be a part of **blsmeta**. Option 
2 will result in authorship on the software paper for **blsmeta** 
(written once students contribute). Options 3-4 will be ongoing 
for undergraduate students. For each option, students will 
learn valuable skills for industry (e.g., data science) and academia 
(e.g., pursing a PhD).

Note also this "lab" exists only in thought, and will hopefully 
come to fruition in the fall of 2022 or 2023.

### Diversity
While I intend to save these projects, 
working with underrepresented students (BIPOC, first-generation, 
students from developing countries, etc.) takes precedence. 
If you are interested in the above options, or have an idea of your own,
please email (drwwilliams@ucdavis.edu) or DM on Twitter 
(https://twitter.com/wdonald_1985). I prefer Twitter.

Women of color and Native Americans are especially encouraged to reach out.