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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 4.5e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.45 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
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#> Chain 1: 
#> Chain 1:  Elapsed Time: 3.709 seconds (Warm-up)
#> Chain 1:                1.993 seconds (Sampling)
#> Chain 1:                5.702 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 3.7e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.37 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
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#> Chain 2: 
#> Chain 2:  Elapsed Time: 3.701 seconds (Warm-up)
#> Chain 2:                3.375 seconds (Sampling)
#> Chain 2:                7.076 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 3.8e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.38 seconds.
#> Chain 3: Adjust your expectations accordingly!
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 3.606 seconds (Warm-up)
#> Chain 3:                2.001 seconds (Sampling)
#> Chain 3:                5.607 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 3.7e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.37 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
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#> Chain 4: 
#> Chain 4:  Elapsed Time: 3.685 seconds (Warm-up)
#> Chain 4:                2.093 seconds (Sampling)
#> Chain 4:                5.778 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 3.6e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.36 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: 3.486 seconds (Warm-up)
#> Chain 1:                1.876 seconds (Sampling)
#> Chain 1:                5.362 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 2.7e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.27 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
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#> Chain 2: 
#> Chain 2:  Elapsed Time: 3.355 seconds (Warm-up)
#> Chain 2:                1.905 seconds (Sampling)
#> Chain 2:                5.26 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 3.5e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.35 seconds.
#> Chain 3: Adjust your expectations accordingly!
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 3.322 seconds (Warm-up)
#> Chain 3:                2.078 seconds (Sampling)
#> Chain 3:                5.4 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 2.7e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.27 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
#> Chain 4: 
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#> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 4: 
#> Chain 4:  Elapsed Time: 3.349 seconds (Warm-up)
#> Chain 4:                1.892 seconds (Sampling)
#> Chain 4:                5.241 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).
# }