Function to set up a multi-membership grouping term in brms. The function does not evaluate its arguments – it exists purely to help set up a model with grouping terms.
Usage
mm(
...,
weights = NULL,
scale = TRUE,
by = NULL,
cor = TRUE,
id = NA,
pw = NULL,
cov = NULL,
dist = "gaussian"
)Arguments
- ...
One or more terms containing grouping factors.
- weights
A matrix specifying the membership weights of each member. It should have as many columns as grouping terms specified in
.... IfNULL(the default), equally weights are used.- scale
Logical; if
TRUE(the default), membership weights are standardized in order to sum to one per row. If negative weights are specified,scaleneeds to be set toFALSE.- by
An optional factor matrix, specifying sub-populations of the groups. It should have as many columns as grouping terms specified in
.... For each level of thebyvariable, a separate variance-covariance matrix will be fitted. Levels of the grouping factor must be nested in levels of thebyvariable matrix.- cor
Logical. If
TRUE(the default), group-level terms will be modelled as correlated.- id
Optional character string. All group-level terms across the model with the same
idwill be modeled as correlated (ifcorisTRUE). Seebrmsformulafor more details.- pw
Optional numeric matrix specifying prior weights. They weight the contribution of each group to the log-prior of the group-level coefficients. Should have as many columns as grouping terms specified in
...and one distinct value for each group level.- cov
An optional matrix which is proportional to the within-group covariance matrix of the group-level effects. All levels of the grouping factor should appear as rownames of the corresponding matrix. This argument can be used, among others, to model pedigrees and phylogenetic effects. See
vignette("brms_phylogenetics")for more details. By default, levels of the same grouping factor are modeled as independent of each other.- dist
Name of the distribution of the group-level effects. Currently
"gaussian"is the only option.
Examples
# \dontrun{
# simulate some data
dat <- data.frame(
y = rnorm(100), x1 = rnorm(100), x2 = rnorm(100),
g1 = sample(1:10, 100, TRUE), g2 = sample(1:10, 100, TRUE)
)
# multi-membership model with two members per group and equal weights
fit1 <- brm(y ~ x1 + (1|mm(g1, g2)), data = dat)
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.3 seconds.
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#> Chain 4:
#> Warning: There were 3 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
summary(fit1)
#> Warning: There were 3 divergent transitions after warmup. Increasing adapt_delta above 0.8 may help. See http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> Family: gaussian
#> Links: mu = identity
#> Formula: y ~ x1 + (1 | mm(g1, g2))
#> Data: dat (Number of observations: 100)
#> Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#> total post-warmup draws = 4000
#>
#> Multilevel Hyperparameters:
#> ~mmg1g2 (Number of levels: 10)
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sd(Intercept) 0.43 0.25 0.04 1.00 1.00 1021 1467
#>
#> Regression Coefficients:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept -0.10 0.19 -0.48 0.29 1.01 1163 1201
#> x1 0.02 0.10 -0.18 0.22 1.00 3946 2827
#>
#> Further Distributional Parameters:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sigma 0.97 0.07 0.85 1.13 1.00 3448 2901
#>
#> Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
#> and Tail_ESS are effective sample size measures, and Rhat is the potential
#> scale reduction factor on split chains (at convergence, Rhat = 1).
# weight the first member two times for than the second member
dat$w1 <- rep(2, 100)
dat$w2 <- rep(1, 100)
fit2 <- brm(y ~ x1 + (1|mm(g1, g2, weights = cbind(w1, w2))), data = dat)
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 2.6e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.26 seconds.
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#> Warning: There were 1 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
summary(fit2)
#> Warning: There were 1 divergent transitions after warmup. Increasing adapt_delta above 0.8 may help. See http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> Family: gaussian
#> Links: mu = identity
#> Formula: y ~ x1 + (1 | mm(g1, g2, weights = cbind(w1, w2)))
#> Data: dat (Number of observations: 100)
#> Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#> total post-warmup draws = 4000
#>
#> Multilevel Hyperparameters:
#> ~mmg1g2 (Number of levels: 10)
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sd(Intercept) 0.40 0.23 0.03 0.94 1.00 1074 1432
#>
#> Regression Coefficients:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept -0.10 0.18 -0.46 0.25 1.00 1339 1118
#> x1 0.02 0.10 -0.18 0.21 1.00 4122 3017
#>
#> Further Distributional Parameters:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sigma 0.97 0.08 0.84 1.13 1.00 3889 2530
#>
#> Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
#> and Tail_ESS are effective sample size measures, and Rhat is the potential
#> scale reduction factor on split chains (at convergence, Rhat = 1).
# multi-membership model with level specific covariate values
dat$xc <- (dat$x1 + dat$x2) / 2
fit3 <- brm(y ~ xc + (1 + mmc(x1, x2) | mm(g1, g2)), data = dat)
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 4.3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.43 seconds.
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#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
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#> Chain 4:
#> Warning: There were 3 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
summary(fit3)
#> Warning: There were 3 divergent transitions after warmup. Increasing adapt_delta above 0.8 may help. See http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> Family: gaussian
#> Links: mu = identity
#> Formula: y ~ xc + (1 + mmc(x1, x2) | mm(g1, g2))
#> Data: dat (Number of observations: 100)
#> Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#> total post-warmup draws = 4000
#>
#> Multilevel Hyperparameters:
#> ~mmg1g2 (Number of levels: 10)
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
#> sd(Intercept) 0.39 0.24 0.03 0.96 1.00 1038
#> sd(mmcx1x2) 0.47 0.26 0.04 1.06 1.00 1280
#> cor(Intercept,mmcx1x2) -0.26 0.50 -0.97 0.82 1.00 1391
#> Tail_ESS
#> sd(Intercept) 1278
#> sd(mmcx1x2) 1096
#> cor(Intercept,mmcx1x2) 1806
#>
#> Regression Coefficients:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept -0.10 0.17 -0.42 0.26 1.00 1725 1651
#> xc -0.37 0.23 -0.85 0.07 1.00 2292 2211
#>
#> Further Distributional Parameters:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sigma 0.92 0.07 0.79 1.07 1.00 2853 2714
#>
#> Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
#> and Tail_ESS are effective sample size measures, and Rhat is the potential
#> scale reduction factor on split chains (at convergence, Rhat = 1).
# }