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Predictors with Measurement Error in brms Models

Source: R/formula-sp.R
me.Rd

(Soft deprecated) Specify predictors with measurement error. The function does not evaluate its arguments – it exists purely to help set up a model.

Usage

me(x, sdx, gr = NULL)

Arguments

x

The variable measured with error.

sdx

Known measurement error of x treated as standard deviation.

gr

Optional grouping factor to specify which values of x correspond to the same value of the latent variable. If NULL (the default) each observation will have its own value of the latent variable.

Details

For detailed documentation see help(brmsformula). me terms are soft deprecated in favor of the more general and consistent mi terms. By default, latent noise-free variables are assumed to be correlated. To change that, add set_mecor(FALSE) to your model formula object (see examples).

See also

brmsformula, brmsformula-helpers

Examples

# \dontrun{
# sample some data
N <- 100
dat <- data.frame(
  y = rnorm(N), x1 = rnorm(N),
  x2 = rnorm(N), sdx = abs(rnorm(N, 1))
 )
# fit a simple error-in-variables model
fit1 <- brm(y ~ me(x1, sdx) + me(x2, sdx), data = dat,
            save_pars = save_pars(latent = TRUE))
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 5.3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.53 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
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#> Chain 1: 
#> Chain 1:  Elapsed Time: 3.864 seconds (Warm-up)
#> Chain 1:                2.075 seconds (Sampling)
#> Chain 1:                5.939 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 3.9e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.39 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
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#> Chain 2: 
#> Chain 2:  Elapsed Time: 3.849 seconds (Warm-up)
#> Chain 2:                3.475 seconds (Sampling)
#> Chain 2:                7.324 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 3.9e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.39 seconds.
#> Chain 3: Adjust your expectations accordingly!
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 3.758 seconds (Warm-up)
#> Chain 3:                2.092 seconds (Sampling)
#> Chain 3:                5.85 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 6.8e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.68 seconds.
#> Chain 4: Adjust your expectations accordingly!
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#> Chain 4: 
#> Chain 4:  Elapsed Time: 3.854 seconds (Warm-up)
#> Chain 4:                2.186 seconds (Sampling)
#> Chain 4:                6.04 seconds (Total)
#> Chain 4: 
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
summary(fit1)
#>  Family: gaussian 
#>   Links: mu = identity 
#> Formula: y ~ me(x1, sdx) + me(x2, sdx) 
#>    Data: dat (Number of observations: 100) 
#>   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#>          total post-warmup draws = 4000
#> 
#> Regression Coefficients:
#>           Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept    -0.03      0.11    -0.25     0.18 1.00     3393     2570
#> mex1sdx       0.35      0.18    -0.00     0.69 1.00     1808     2707
#> mex2sdx      -0.01      0.20    -0.39     0.37 1.00     2100     2972
#> 
#> Further Distributional Parameters:
#>       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sigma     1.00      0.08     0.86     1.17 1.00     2503     2446
#> 
#> 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).

# turn off modeling of correlations
bform <- bf(y ~ me(x1, sdx) + me(x2, sdx)) + set_mecor(FALSE)
fit2 <- brm(bform, data = dat, save_pars = save_pars(latent = TRUE))
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 4e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.4 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 3.701 seconds (Warm-up)
#> Chain 1:                2.014 seconds (Sampling)
#> Chain 1:                5.715 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 3.3e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.33 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
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#> Chain 2: 
#> Chain 2:  Elapsed Time: 3.521 seconds (Warm-up)
#> Chain 2:                1.976 seconds (Sampling)
#> Chain 2:                5.497 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 3.3e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.33 seconds.
#> Chain 3: Adjust your expectations accordingly!
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 3.435 seconds (Warm-up)
#> Chain 3:                2.165 seconds (Sampling)
#> Chain 3:                5.6 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 3.3e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.33 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
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#> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 4: 
#> Chain 4:  Elapsed Time: 3.476 seconds (Warm-up)
#> Chain 4:                1.975 seconds (Sampling)
#> Chain 4:                5.451 seconds (Total)
#> Chain 4: 
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
summary(fit2)
#>  Family: gaussian 
#>   Links: mu = identity 
#> Formula: y ~ me(x1, sdx) + me(x2, sdx) 
#>    Data: dat (Number of observations: 100) 
#>   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#>          total post-warmup draws = 4000
#> 
#> Regression Coefficients:
#>           Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept    -0.03      0.10    -0.23     0.17 1.00     3560     3154
#> mex1sdx       0.35      0.17     0.01     0.68 1.00     2007     2790
#> mex2sdx      -0.00      0.19    -0.37     0.38 1.00     1940     2717
#> 
#> Further Distributional Parameters:
#>       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sigma     1.00      0.08     0.86     1.17 1.00     3077     2533
#> 
#> 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).
# }