Calculate Akaike weights

12 files changed, 361 insertions, 11 deletions

diff --git a/NAMESPACE b/NAMESPACE
index e561621b..26995055 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -3,6 +3,8 @@
 S3method("[",mmkin)
 S3method(AIC,mmkin)
 S3method(BIC,mmkin)
+S3method(aw,mkinfit)
+S3method(aw,mmkin)
 S3method(confint,mkinfit)
 S3method(loftest,mkinfit)
 S3method(logLik,mkinfit)
@@ -30,6 +32,7 @@ export(IORE.solution)
 export(SFO.solution)
 export(SFORB.solution)
 export(add_err)
+export(aw)
 export(backtransform_odeparms)
 export(endpoints)
 export(ilr)
diff --git a/NEWS.md b/NEWS.md
index 965105f4..28cf76ad 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,7 @@
 # mkin 0.9.49.8 (unreleased)
 
+- 'aw': Generic function for calculating Akaike weights, methods for mkinfit objects and mmkin columns
+
 - 'loftest': Add a lack-of-fit test
 
 - 'plot_res', 'plot_sep' and 'mkinerrplot': Add the possibility to show standardized residuals and make it the default for fits with error models other than 'const'
diff --git a/R/aw.R b/R/aw.R
new file mode 100644
index 00000000..24078f38
--- /dev/null
+++ b/R/aw.R
@@ -0,0 +1,60 @@
+#' Calculate Akaike weights for model averaging
+#'
+#' Akaike weights are calculated based on the relative
+#' expected Kullback-Leibler information as specified
+#' by Burnham and Anderson (2004).
+#'
+#' @param object An mmkin column object, containing two or more
+#'   \code{\link{mkinfit}} models that have been fitted to the same data,
+#'   or an mkinfit object. In the latter case, further mkinfit
+#'   objects fitted to the same data should be specified
+#'   as dots arguments.
+#' @param \dots Not used in the method for mmkin column objects,
+#'   further mkinfit objects in the method for mkinfit objects.
+#' @references Burnham KP and Anderson DR (2004) Multimodel
+#'   Inference: Understanding AIC and BIC in Model Selection
+#'   Sociological Methods & Research 33(2) 261-304
+#' @examples
+#' \dontrun{
+#' f_sfo <- mkinfit("SFO", FOCUS_2006_D, quiet = TRUE)
+#' f_dfop <- mkinfit("DFOP", FOCUS_2006_D, quiet = TRUE)
+#' aw_sfo_dfop <- aw(f_sfo, f_dfop)
+#' sum(aw_sfo_dfop)
+#' aw_sfo_dfop # SFO gets more weight as it has less parameters and a similar fit
+#' f <- mmkin(c("SFO", "FOMC", "DFOP"), list("FOCUS D" = FOCUS_2006_D), cores = 1, quiet = TRUE)
+#' aw(f)
+#' sum(aw(f))
+#' aw(f[c("SFO", "DFOP")])
+#' }
+#' @export
+aw <- function(object, ...) UseMethod("aw")
+
+#' @export
+#' @rdname aw
+aw.mkinfit <- function(object, ...) {
+  oo <- list(...)
+  data_object <- object$data[c("time", "variable", "observed")]
+  for (i in seq_along(oo)) {
+    if (!inherits(oo[[i]], "mkinfit")) stop("Please supply only mkinfit objects")
+    data_other_object <- oo[[i]]$data[c("time", "variable", "observed")]
+    if (!identical(data_object, data_other_object)) {
+      stop("It seems that the mkinfit objects have not all been fitted to the same data")
+    }
+  }
+  all_objects <- list(object, ...)
+  AIC_all <- sapply(all_objects, AIC)
+  delta_i <- AIC_all - min(AIC_all)
+  denom <- sum(exp(-delta_i/2))
+  w_i <- exp(-delta_i/2) / denom
+  return(w_i)
+}
+
+#' @export
+#' @rdname aw
+aw.mmkin <- function(object, ...) {
+  if (ncol(object) > 1) stop("Please supply an mmkin column object")
+  do.call(aw, object)
+}
+
+
+
diff --git a/_pkgdown.yml b/_pkgdown.yml
index c298256f..6bb05b3e 100644
--- a/_pkgdown.yml
+++ b/_pkgdown.yml
@@ -25,6 +25,7 @@ reference:
       - loftest
       - mkinerrmin
       - endpoints
+      - aw
       - CAKE_export
   - title: Work with mmkin objects
     desc: Functions working with aggregated results
diff --git a/docs/news/index.html b/docs/news/index.html
index 9aa2e18b..6b0b89fa 100644
--- a/docs/news/index.html
+++ b/docs/news/index.html
@@ -134,6 +134,7 @@
 <a href="#mkin-0-9-49-8-unreleased" class="anchor"></a>mkin 0.9.49.8 (unreleased)<small> Unreleased </small>
 </h1>
 <ul>
+<li><p>‘aw’: Generic function for calculating Akaike weights, methods for mkinfit objects and mmkin columns</p></li>
 <li><p>‘loftest’: Add a lack-of-fit test</p></li>
 <li><p>‘plot_res’, ‘plot_sep’ and ‘mkinerrplot’: Add the possibility to show standardized residuals and make it the default for fits with error models other than ‘const’</p></li>
 <li><p>‘lrtest.mkinfit’: Improve naming of the compared fits in the case of fixed parameters</p></li>
diff --git a/docs/reference/aw.html b/docs/reference/aw.html
new file mode 100644
index 00000000..b6f3ce48
--- /dev/null
+++ b/docs/reference/aw.html
@@ -0,0 +1,214 @@
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+expected Kullback-Leibler information as specified
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+  <div class="col-md-9 contents">
+    <div class="page-header">
+    <h1>Calculate Akaike weights for model averaging</h1>
+    
+    <div class="hidden name"><code>aw.Rd</code></div>
+    </div>
+
+    <div class="ref-description">
+    <p>Akaike weights are calculated based on the relative
+expected Kullback-Leibler information as specified
+by Burnham and Anderson (2004).</p>
+    </div>
+
+    <pre class="usage"><span class='fu'>aw</span>(<span class='no'>object</span>, <span class='no'>...</span>)
+
+<span class='co'># S3 method for mkinfit</span>
+<span class='fu'>aw</span>(<span class='no'>object</span>, <span class='no'>...</span>)
+
+<span class='co'># S3 method for mmkin</span>
+<span class='fu'>aw</span>(<span class='no'>object</span>, <span class='no'>...</span>)</pre>
+
+    <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
+    <table class="ref-arguments">
+    <colgroup><col class="name" /><col class="desc" /></colgroup>
+    <tr>
+      <th>object</th>
+      <td><p>An mmkin column object, containing two or more
+<code><a href='mkinfit.html'>mkinfit</a></code> models that have been fitted to the same data,
+or an mkinfit object. In the latter case, further mkinfit
+objects fitted to the same data should be specified
+as dots arguments.</p></td>
+    </tr>
+    <tr>
+      <th>...</th>
+      <td><p>Not used in the method for mmkin column objects,
+further mkinfit objects in the method for mkinfit objects.</p></td>
+    </tr>
+    </table>
+
+    <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
+
+    <p>Burnham KP and Anderson DR (2004) Multimodel
+  Inference: Understanding AIC and BIC in Model Selection
+  Sociological Methods &amp; Research 33(2) 261-304</p>
+
+    <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
+    <pre class="examples"><div class='input'><span class='co'># \dontrun{</span>
+<span class='no'>f_sfo</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"SFO"</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
+<span class='no'>f_dfop</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"DFOP"</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
+<span class='no'>aw_sfo_dfop</span> <span class='kw'>&lt;-</span> <span class='fu'>aw</span>(<span class='no'>f_sfo</span>, <span class='no'>f_dfop</span>)
+<span class='fu'><a href='https://rdrr.io/r/base/sum.html'>sum</a></span>(<span class='no'>aw_sfo_dfop</span>)</div><div class='output co'>#&gt; [1] 1</div><div class='input'><span class='no'>aw_sfo_dfop</span> <span class='co'># SFO gets more weight as it has less parameters and a similar fit</span></div><div class='output co'>#&gt; [1] 0.5970258 0.4029742</div><div class='input'><span class='no'>f</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"FOMC"</span>, <span class='st'>"DFOP"</span>), <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='st'>"FOCUS D"</span> <span class='kw'>=</span> <span class='no'>FOCUS_2006_D</span>), <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
+<span class='fu'>aw</span>(<span class='no'>f</span>)</div><div class='output co'>#&gt; [1] 0.4808722 0.1945539 0.3245740</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/sum.html'>sum</a></span>(<span class='fu'>aw</span>(<span class='no'>f</span>))</div><div class='output co'>#&gt; [1] 1</div><div class='input'><span class='fu'>aw</span>(<span class='no'>f</span>[<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"DFOP"</span>)])</div><div class='output co'>#&gt; [1] 0.5970258 0.4029742</div><div class='input'># }
+</div></pre>
+  </div>
+  <div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
+    <h2>Contents</h2>
+    <ul class="nav nav-pills nav-stacked">
+      <li><a href="#arguments">Arguments</a></li>
+      <li><a href="#references">References</a></li>
+      <li><a href="#examples">Examples</a></li>
+    </ul>
+
+  </div>
+</div>
+
+
+      <footer>
+      <div class="copyright">
+  <p>Developed by Johannes Ranke.</p>
+</div>
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diff --git a/docs/reference/index.html b/docs/reference/index.html
index 4398469b..3d417267 100644
--- a/docs/reference/index.html
+++ b/docs/reference/index.html
@@ -234,6 +234,12 @@ with mkinfit</p></td>
       </tr><tr>
         
         <td>
+          <p><code><a href="aw.html">aw()</a></code> </p>
+        </td>
+        <td><p>Calculate Akaike weights for model averaging</p></td>
+      </tr><tr>
+        
+        <td>
           <p><code><a href="CAKE_export.html">CAKE_export()</a></code> </p>
         </td>
         <td><p>Export a list of datasets format to a CAKE study file</p></td>
diff --git a/docs/sitemap.xml b/docs/sitemap.xml
index 66b776b2..a8d6dfa4 100644
--- a/docs/sitemap.xml
+++ b/docs/sitemap.xml
@@ -55,6 +55,9 @@
     <loc>https://pkgdown.jrwb.de/mkin/reference/add_err.html</loc>
   </url>
   <url>
+    <loc>https://pkgdown.jrwb.de/mkin/reference/aw.html</loc>
+  </url>
+  <url>
     <loc>https://pkgdown.jrwb.de/mkin/reference/confint.mkinfit.html</loc>
   </url>
   <url>
diff --git a/man/aw.Rd b/man/aw.Rd
new file mode 100644
index 00000000..f0994b94
--- /dev/null
+++ b/man/aw.Rd
@@ -0,0 +1,47 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/aw.R
+\name{aw}
+\alias{aw}
+\alias{aw.mkinfit}
+\alias{aw.mmkin}
+\title{Calculate Akaike weights for model averaging}
+\usage{
+aw(object, ...)
+
+\method{aw}{mkinfit}(object, ...)
+
+\method{aw}{mmkin}(object, ...)
+}
+\arguments{
+\item{object}{An mmkin column object, containing two or more
+\code{\link{mkinfit}} models that have been fitted to the same data,
+or an mkinfit object. In the latter case, further mkinfit
+objects fitted to the same data should be specified
+as dots arguments.}
+
+\item{\dots}{Not used in the method for mmkin column objects,
+further mkinfit objects in the method for mkinfit objects.}
+}
+\description{
+Akaike weights are calculated based on the relative
+expected Kullback-Leibler information as specified
+by Burnham and Anderson (2004).
+}
+\examples{
+\dontrun{
+f_sfo <- mkinfit("SFO", FOCUS_2006_D, quiet = TRUE)
+f_dfop <- mkinfit("DFOP", FOCUS_2006_D, quiet = TRUE)
+aw_sfo_dfop <- aw(f_sfo, f_dfop)
+sum(aw_sfo_dfop)
+aw_sfo_dfop # SFO gets more weight as it has less parameters and a similar fit
+f <- mmkin(c("SFO", "FOMC", "DFOP"), list("FOCUS D" = FOCUS_2006_D), cores = 1, quiet = TRUE)
+aw(f)
+sum(aw(f))
+aw(f[c("SFO", "DFOP")])
+}
+}
+\references{
+Burnham KP and Anderson DR (2004) Multimodel
+  Inference: Understanding AIC and BIC in Model Selection
+  Sociological Methods & Research 33(2) 261-304
+}
diff --git a/test.log b/test.log
index bc6d26ae..c51d06b8 100644
--- a/test.log
+++ b/test.log
@@ -1,11 +1,12 @@
 Loading mkin
 Testing mkin
 ✔ |  OK F W S | Context
+✔ |   5       | Calculation of Akaike weights
 ✔ |   2       | Export dataset for reading into CAKE
-✔ |  10       | Confidence intervals and p-values [10.1 s]
-✔ |  14       | Error model fitting [40.5 s]
+✔ |  10       | Confidence intervals and p-values [9.7 s]
+✔ |  14       | Error model fitting [36.9 s]
 ✔ |   4       | Calculation of FOCUS chi2 error levels [2.2 s]
-✔ |  13       | Results for FOCUS D established in expertise for UBA (Ranke 2014) [3.4 s]
+✔ |  13       | Results for FOCUS D established in expertise for UBA (Ranke 2014) [3.3 s]
 ✔ |   6       | Test fitting the decline of metabolites from their maximum [0.7 s]
 ✔ |   1       | Fitting the logistic model [0.9 s]
 ✔ |   1       | Test dataset class mkinds used in gmkin
@@ -18,20 +19,20 @@ Testing mkin
 ✔ |  11       | Plotting [0.6 s]
 ✔ |   4       | AIC calculation
 ✔ |   2       | Residuals extracted from mkinfit models
-✔ |   2       | Complex test case from Schaefer et al. (2007) Piacenza paper [5.6 s]
-✔ |   4       | Fitting the SFORB model [1.8 s]
+✔ |   2       | Complex test case from Schaefer et al. (2007) Piacenza paper [5.3 s]
+✔ |   4       | Fitting the SFORB model [1.7 s]
 ✔ |   1       | Summaries of old mkinfit objects
-✔ |   4       | Results for synthetic data established in expertise for UBA (Ranke 2014) [7.5 s]
-✔ |   7     1 | Hypothesis tests [34.1 s]
+✔ |   4       | Results for synthetic data established in expertise for UBA (Ranke 2014) [7.2 s]
+✔ |   7     1 | Hypothesis tests [32.3 s]
 ────────────────────────────────────────────────────────────────────────────────
-test_tests.R:59: skip: We can do a likelihood ratio test using an update specification
+test_tests.R:60: skip: We can do a likelihood ratio test using an update specification
 Reason: This errors out if called by testthat while it works in a normal R session
 ────────────────────────────────────────────────────────────────────────────────
 
 ══ Results ═════════════════════════════════════════════════════════════════════
-Duration: 116.9 s
+Duration: 110.2 s
 
-OK:       133
+OK:       138
 Failed:   0
 Warnings: 0
 Skipped:  1
diff --git a/tests/testthat/FOCUS_2006_D.csf b/tests/testthat/FOCUS_2006_D.csf
index 09940aa3..358b50e3 100644
--- a/tests/testthat/FOCUS_2006_D.csf
+++ b/tests/testthat/FOCUS_2006_D.csf
@@ -5,7 +5,7 @@ Description:
 MeasurementUnits: % AR
 TimeUnits: days
 Comments: Created using mkin::CAKE_export
-Date: 2019-11-09
+Date: 2019-11-13
 Optimiser: IRLS
 
 [Data]
diff --git a/tests/testthat/test_aw.R b/tests/testthat/test_aw.R
new file mode 100644
index 00000000..0a493893
--- /dev/null
+++ b/tests/testthat/test_aw.R
@@ -0,0 +1,12 @@
+context("Calculation of Akaike weights")
+
+test_that("Akaike weights sum to one", {
+  skip_on_cran()
+  aw_1 <- aw(fit_nw_1, fit_obs_1, fit_tc_1)
+  expect_error(aw(fit_nw_1, f_2_mkin), "same data")
+  expect_error(aw(fit_nw_1, 3), "mkinfit objects")
+  expect_equal(sum(aw_1), 1)
+  aw_2 <- aw(fits[c("SFO", "DFOP"), "FOCUS_D"])
+  expect_equal(sum(aw_2), 1)
+  expect_error(aw(fits), "mmkin column object")
+})