<h1>Make Power Fun (Again?)</h1> <h2>Brandon LeBeau</h2> <h3>University of Iowa</h3> # Overview 1. (G)LMMs 2. Power 3. `simglm` package 4. Shiny Demo - Broken! # Linear Mixed Model (LMM) ![](/figs/equations.png) # Power - Power is the ability to statistically detect a true effect (i.e. non-zero population effect). - For simple models (e.g. t-tests, regression) there are closed form equations for generating power. + R has routines for these: `power.t.test, power.anova.test` + Gpower3 # Power Example ```r n <- seq(4, 1000, 2) power <- sapply(seq_along(n), function(i) power.t.test(n = n[i], delta = .15, sd = 1, type = 'two.sample')\$power) ``` ![](/figs/power_plot-1.png) # Power for (G)LMM - Power for more complex models is not as straightforward; + particularly with messy real world data. - There is software for GLMM models to generate power: + Optimal Design: <http://hlmsoft.net/od/> + MLPowSim: <http://www.bristol.ac.uk/cmm/software/mlpowsim/> + Snijders, *Power and Sample Size in Multilevel Linear Models*. # Power is hard - In practice, power is hard. - Need to make many assumptions on data that has not been collected. + Therefore, data assumptions made for power computations will likely differ from collected sample. - A power analysis needs to be flexible, exploratory, and well thought out. # Power is Fun? - Three common reasons to do power analysis: 1. Power evidence for grant/planning 2. Post Hoc to explore insignificant results 3. Monte Carlo studies # `simglm` Overview - `simglm` aims to simulate (G)LMMs with up to three levels of nesting (aim to add more later). - Flexible data generation allows: + any number of covariates and discrete covariates + change distribution of continuous covariates + change random distribution + unbalanced data + missing data + serial correlation # Power with `simglm` - Power with `simglm` takes on a Monte Carlo approach + This can provide a more thorough analysis/understanding of power. - Always outputs a data frame + Useful for plotting + Data manipulation + etc. - Serves as a wrapper around data generation process. # Power Analysis with `simglm` - Factorial Design: 1. Idenfity factors that influences power 2. Determine number of replications 3. Explore results - Future Development 1. Add ability for data generation and power model to differ # Simple Example - Suppose we wished to generate data for a simple logistic regression. ```r library(simglm) fixed <- ~ 1 + act + diff fixed_param <- c(0.1, 0.5, 0.3) cov_param <- list(dist_fun = c('rnorm', 'rnorm'), var_type = c("single", "single"), opts = list(list(mean = 0, sd = 2), list(mean = 0, sd = 4))) n <- 50 temp_single <- sim_glm(fixed = fixed, fixed_param = fixed_param, cov_param = cov_param, n = n, data_str = "single") ``` # Output ```r head(temp_single) ``` ``` ## X.Intercept. act diff Fbeta logistic sim_data ID ## 1 1 -0.02913722 -0.4430546 -0.04748497 0.4881310 1 1 ## 2 1 0.66199364 2.1443743 1.07430910 0.7454155 1 2 ## 3 1 1.44621026 -1.1909231 0.46582819 0.6143959 0 3 ## 4 1 -0.26011629 3.4395304 1.00180096 0.7314125 0 4 ## 5 1 -0.09984213 0.8485436 0.30464201 0.5755769 1 5 ## 6 1 -2.72704127 3.3246515 -0.26612517 0.4338586 0 6 ``` # Simple Power Analysis - Suppose we wish to use the same generating model for a power analysis ```r pow_param <- c('(Intercept)', 'act', 'diff') alpha <- .01 pow_dist <- "z" pow_tail <- 2 replicates <- 100 power_out <- sim_pow_glm(fixed = fixed, fixed_param = fixed_param, cov_param = cov_param, n = n, data_str = "single", pow_param = pow_param, alpha = alpha, pow_dist = pow_dist, pow_tail = pow_tail, replicates = replicates) ``` # Output ```r power_out ``` ``` ## # A tibble: 3 × 6 ## var avg_test_stat sd_test_stat power num_reject num_repl ## <fctr> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 (Intercept) 0.878713 0.6709319 0.01 1 100 ## 2 act 2.342617 0.5777646 0.34 34 100 ## 3 diff 2.609432 0.5506204 0.56 56 100 ``` # Varying Arguments - Now suppose we wish to vary the following arguments: - Vary n - 50 vs 150 - vary effect size on diff - .3 vs .45 ```r terms_vary <- list(n = c(50, 150), fixed_param = list(c(0.1, 0.5, 0.3), c(0.1, 0.5, 0.45))) power_out <- sim_pow_glm(fixed = fixed, fixed_param = fixed_param, cov_param = cov_param, n = n, data_str = "single", pow_param = pow_param, alpha = alpha, pow_dist = pow_dist, pow_tail = pow_tail, replicates = replicates, terms_vary = terms_vary) ``` # Output ```r power_out ``` ``` ## Source: local data frame [12 x 8] ## Groups: var, n [?] ## ## var n fixed_param avg_test_stat sd_test_stat power ## <fctr> <dbl> <fctr> <dbl> <dbl> <dbl> ## 1 (Intercept) 50 0.1,0.5,0.3 0.7778328 0.5863240 0.00 ## 2 (Intercept) 50 0.1,0.5,0.45 0.8364212 0.6377631 0.01 ## 3 (Intercept) 150 0.1,0.5,0.3 0.8629973 0.5814426 0.00 ## 4 (Intercept) 150 0.1,0.5,0.45 0.9183353 0.6879182 0.01 ## 5 act 50 0.1,0.5,0.3 2.4246997 0.6222346 0.44 ## 6 act 50 0.1,0.5,0.45 2.2247451 0.6688308 0.34 ## 7 act 150 0.1,0.5,0.3 4.3196568 0.6233962 0.99 ## 8 act 150 0.1,0.5,0.45 3.9515646 0.6332452 0.97 ## 9 diff 50 0.1,0.5,0.3 2.7887204 0.4892985 0.73 ## 10 diff 50 0.1,0.5,0.45 3.0747886 0.3988745 0.89 ## 11 diff 150 0.1,0.5,0.3 4.7892881 0.5025082 1.00 ## 12 diff 150 0.1,0.5,0.45 5.6060130 0.2823105 1.00 ## # ... with 2 more variables: num_reject <dbl>, num_repl <dbl> ``` # Move to Mixed Models - It is simple to move from single level to multilevel or mixed models. ```r fixed <- ~1 + time + diff + act + time:act random <- ~1 + time fixed_param <- c(0, 0.2, 0.1, 0.3, 0.05) random_param <- list(random_var = c(3, 2), rand_gen = "rnorm") cov_param <- list(dist_fun = c('rnorm', 'rnorm'), var_type = c("lvl1", "lvl2"), opts = list(list(mean = 0, sd = 3), list(mean = 0, sd = 2))) n <- 50 p <- 6 data_str <- "long" temp_long <- sim_glm(fixed = fixed, random = random, fixed_param = fixed_param, random_param = random_param, cov_param = cov_param, n = n, p = p, k = NULL, data_str = data_str) ``` # Output ```r head(temp_long) ``` ``` ## X.Intercept. time diff act time.act b0 b1 ## 1 1 0 -6.76572749 -0.3932853 0.0000000 -1.947485 -2.295427 ## 2 1 1 0.15530420 -0.3932853 -0.3932853 -1.947485 -2.295427 ## 3 1 2 0.07605058 -0.3932853 -0.7865707 -1.947485 -2.295427 ## 4 1 3 -1.11192544 -0.3932853 -1.1798560 -1.947485 -2.295427 ## 5 1 4 -4.17141062 -0.3932853 -1.5731413 -1.947485 -2.295427 ## 6 1 5 4.77024867 -0.3932853 -1.9664267 -1.947485 -2.295427 ## Fbeta randEff logistic prob sim_data withinID clustID ## 1 -0.79455835 -1.947485 -2.742044 6.053757e-02 0 1 1 ## 2 0.07788055 -4.242913 -4.165032 1.529175e-02 0 2 1 ## 3 0.25029093 -6.538340 -6.288049 1.854935e-03 0 3 1 ## 4 0.31182906 -8.833767 -8.521938 1.990136e-04 0 4 1 ## 5 0.18621627 -11.129195 -10.942978 1.768142e-05 0 5 1 ## 6 1.26071793 -13.424622 -12.163904 5.215325e-06 0 6 1 ``` # Doing Power - Power is also easily extended. ```r pow_param <- c('time', 'diff', 'act') alpha <- .01 pow_dist <- "z" pow_tail <- 2 replicates <- 20 power_out <- sim_pow_glm(fixed = fixed, random = random, fixed_param = fixed_param, random_param = random_param, cov_param = cov_param, k = NULL, n = n, p = p, data_str = data_str, unbal = FALSE, pow_param = pow_param, alpha = alpha, pow_dist = pow_dist, pow_tail = pow_tail, replicates = replicates) ``` # Output ```r power_out ``` ``` ## # A tibble: 3 × 6 ## var avg_test_stat sd_test_stat power num_reject num_repl ## <fctr> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 act 12.06197 46.70227 0.20 4 20 ## 2 diff 11.89673 45.13827 0.25 5 20 ## 3 time 18.78877 79.36869 0.05 1 20 ``` # Vary Arguments - Perhaps our effect size estimate is conservative. ```r terms_vary <- list(fixed_param = list(c(0, 0.2, 0.1, 0.3, 0.05), c(0, 0.2, 0.3, 0.3, 0.05))) power_out <- sim_pow_glm(fixed = fixed, random = random, fixed_param = fixed_param, random_param = random_param, cov_param = cov_param, k = NULL, n = n, p = p, data_str = data_str, unbal = FALSE, pow_param = pow_param, alpha = alpha, pow_dist = pow_dist, pow_tail = pow_tail, replicates = replicates, terms_vary = terms_vary) ``` # Output ```r power_out ``` ``` ## Source: local data frame [6 x 7] ## Groups: var [?] ## ## var fixed_param avg_test_stat sd_test_stat power num_reject ## <fctr> <fctr> <dbl> <dbl> <dbl> <dbl> ## 1 act 0,0.2,0.1,0.3,0.05 1.1914255 0.8114762 0.10 2 ## 2 act 0,0.2,0.3,0.3,0.05 22.9059014 96.3531136 0.15 3 ## 3 diff 0,0.2,0.1,0.3,0.05 1.3071639 0.8681348 0.05 1 ## 4 diff 0,0.2,0.3,0.3,0.05 17.4774138 62.2814403 0.95 19 ## 5 time 0,0.2,0.1,0.3,0.05 0.9281452 0.7670600 0.05 1 ## 6 time 0,0.2,0.3,0.3,0.05 12.1678311 49.9607401 0.05 1 ## # ... with 1 more variables: num_repl <dbl> ``` # Shiny App - Note: This app currently looks nice, but is utterly broken! ```r shiny::runGitHub('simglm', username = 'lebebr01', subdir = 'inst/shiny_examples/demo') ``` or ```r devtools::install_github('lebebr01/simglm') library(simglm) run_shiny() ``` - Must have following packages installed: `simglm, shiny, shinydashboard, ggplot2, lme4, DT`. # `simglm` timeline - Aim to have this package submitted to CRAN by the end of March. - Fix Shiny application. - For now look for the package on GitHub <http://github.com/lebebr01/simglm> # Questions? - Twitter: @blebeau11 - Website: <http://brandonlebeau.org> - Slides: <http://brandonlebeau.org/2017/02/24/csp2017.html> - GitHub: <http://github.com/lebebr01/simglm>