-
Notifications
You must be signed in to change notification settings - Fork 3
/
overview.html
580 lines (511 loc) · 20.2 KB
/
overview.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<title>Analysis of GPWGv3 Data Using R</title>
<script src="site_libs/header-attrs-2.21/header-attrs.js"></script>
<script src="site_libs/jquery-3.6.0/jquery-3.6.0.min.js"></script>
<meta name="viewport" content="width=device-width, initial-scale=1" />
<link href="site_libs/bootstrap-3.3.5/css/united.min.css" rel="stylesheet" />
<script src="site_libs/bootstrap-3.3.5/js/bootstrap.min.js"></script>
<script src="site_libs/bootstrap-3.3.5/shim/html5shiv.min.js"></script>
<script src="site_libs/bootstrap-3.3.5/shim/respond.min.js"></script>
<style>h1 {font-size: 34px;}
h1.title {font-size: 38px;}
h2 {font-size: 30px;}
h3 {font-size: 24px;}
h4 {font-size: 18px;}
h5 {font-size: 16px;}
h6 {font-size: 12px;}
code {color: inherit; background-color: rgba(0, 0, 0, 0.04);}
pre:not([class]) { background-color: white }</style>
<script src="site_libs/navigation-1.1/tabsets.js"></script>
<style type="text/css">
code{white-space: pre-wrap;}
span.smallcaps{font-variant: small-caps;}
span.underline{text-decoration: underline;}
div.column{display: inline-block; vertical-align: top; width: 50%;}
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
ul.task-list{list-style: none;}
</style>
<link rel="stylesheet" href="SI-md-08.css" type="text/css" />
<style type = "text/css">
.main-container {
max-width: 940px;
margin-left: auto;
margin-right: auto;
}
img {
max-width:100%;
}
.tabbed-pane {
padding-top: 12px;
}
.html-widget {
margin-bottom: 20px;
}
button.code-folding-btn:focus {
outline: none;
}
summary {
display: list-item;
}
details > summary > p:only-child {
display: inline;
}
pre code {
padding: 0;
}
</style>
<style type="text/css">
.dropdown-submenu {
position: relative;
}
.dropdown-submenu>.dropdown-menu {
top: 0;
left: 100%;
margin-top: -6px;
margin-left: -1px;
border-radius: 0 6px 6px 6px;
}
.dropdown-submenu:hover>.dropdown-menu {
display: block;
}
.dropdown-submenu>a:after {
display: block;
content: " ";
float: right;
width: 0;
height: 0;
border-color: transparent;
border-style: solid;
border-width: 5px 0 5px 5px;
border-left-color: #cccccc;
margin-top: 5px;
margin-right: -10px;
}
.dropdown-submenu:hover>a:after {
border-left-color: #adb5bd;
}
.dropdown-submenu.pull-left {
float: none;
}
.dropdown-submenu.pull-left>.dropdown-menu {
left: -100%;
margin-left: 10px;
border-radius: 6px 0 6px 6px;
}
</style>
<script type="text/javascript">
// manage active state of menu based on current page
$(document).ready(function () {
// active menu anchor
href = window.location.pathname
href = href.substr(href.lastIndexOf('/') + 1)
if (href === "")
href = "index.html";
var menuAnchor = $('a[href="' + href + '"]');
// mark the anchor link active (and if it's in a dropdown, also mark that active)
var dropdown = menuAnchor.closest('li.dropdown');
if (window.bootstrap) { // Bootstrap 4+
menuAnchor.addClass('active');
dropdown.find('> .dropdown-toggle').addClass('active');
} else { // Bootstrap 3
menuAnchor.parent().addClass('active');
dropdown.addClass('active');
}
// Navbar adjustments
var navHeight = $(".navbar").first().height() + 15;
var style = document.createElement('style');
var pt = "padding-top: " + navHeight + "px; ";
var mt = "margin-top: -" + navHeight + "px; ";
var css = "";
// offset scroll position for anchor links (for fixed navbar)
for (var i = 1; i <= 6; i++) {
css += ".section h" + i + "{ " + pt + mt + "}\n";
}
style.innerHTML = "body {" + pt + "padding-bottom: 40px; }\n" + css;
document.head.appendChild(style);
});
</script>
<!-- tabsets -->
<style type="text/css">
.tabset-dropdown > .nav-tabs {
display: inline-table;
max-height: 500px;
min-height: 44px;
overflow-y: auto;
border: 1px solid #ddd;
border-radius: 4px;
}
.tabset-dropdown > .nav-tabs > li.active:before, .tabset-dropdown > .nav-tabs.nav-tabs-open:before {
content: "\e259";
font-family: 'Glyphicons Halflings';
display: inline-block;
padding: 10px;
border-right: 1px solid #ddd;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open > li.active:before {
content: "\e258";
font-family: 'Glyphicons Halflings';
border: none;
}
.tabset-dropdown > .nav-tabs > li.active {
display: block;
}
.tabset-dropdown > .nav-tabs > li > a,
.tabset-dropdown > .nav-tabs > li > a:focus,
.tabset-dropdown > .nav-tabs > li > a:hover {
border: none;
display: inline-block;
border-radius: 4px;
background-color: transparent;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open > li {
display: block;
float: none;
}
.tabset-dropdown > .nav-tabs > li {
display: none;
}
</style>
<!-- code folding -->
</head>
<body>
<div class="container-fluid main-container">
<div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-bs-toggle="collapse" data-target="#navbar" data-bs-target="#navbar">
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="index.html">GCDv3 Analysis</a>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="overview.html">Overview</a>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
Analyses
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li class="dropdown-header">Standard analysis</li>
<li>
<a href="mdb-to-csv_07.html">Query and site .csv files from an Access database (mdb-to-csv.R)</a>
</li>
<li>
<a href="trans-and-zscore_07.html">Box-Cox transformation and Z-Score rescaling (trans-and-zscore.R)</a>
</li>
<li>
<a href="presample-bin_07.html">Presampling or binning of transformed data (presample-bin.R)</a>
</li>
<li>
<a href="smooth-curve_07.html">Composite curves and bootstrap C.I.'s using locfit() (smooth-curve.R)</a>
</li>
<li class="dropdown-header">Alternative approaches</li>
<li>
<a href="trans-and-norman_10.html">Box-Cox transformation and normalized anomaly rescaling (trans-and-norman.R)</a>
</li>
<li>
<a href="bin-boot_10.html">Composite curves and bootstrap C.I.'s via binning</a>
</li>
</ul>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
Code
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li class="dropdown-header">Standard analysis</li>
<li>
<a href="mdb-to-csv_07_code.html">mdb-to-csv_code.R</a>
</li>
<li>
<a href="trans-and-zscore_07_code.html">trans-and-zscore.R</a>
</li>
<li>
<a href="presample-bin_07_code.html">presample-bin.R</a>
</li>
<li>
<a href="smooth-curve_07_code.html">smooth-curve.R</a>
</li>
<li class="dropdown-header">Alternative approaches</li>
<li>
<a href="mdb-to-csv_07_code_osx.html">mdb-to-csv_code_osx.R</a>
</li>
<li>
<a href="trans-and-norman_10_code.html">trans-and-norman.R</a>
</li>
<li>
<a href="bin-boot_10_code.html">bin-boot.R</a>
</li>
</ul>
</li>
</ul>
<ul class="nav navbar-nav navbar-right">
</ul>
</div><!--/.nav-collapse -->
</div><!--/.container -->
</div><!--/.navbar -->
<div id="header">
<h1 class="title toc-ignore">Analysis of GPWGv3 Data Using R</h1>
</div>
<div id="TOC">
<ul>
<li><a href="#introduction" id="toc-introduction">Introduction</a></li>
<li><a href="#data" id="toc-data">Data</a></li>
<li><a href="#analysis-steps" id="toc-analysis-steps">Analysis steps</a>
<ul>
<li><a href="#query-and-site-.csv-files"
id="toc-query-and-site-.csv-files">1 Query and site .csv files</a></li>
<li><a href="#transformation-and-standardizationanomalization"
id="toc-transformation-and-standardizationanomalization">2
Transformation and standardization/anomalization</a></li>
<li><a href="#presamplingprebinning" id="toc-presamplingprebinning">3
Presampling/prebinning</a></li>
<li><a href="#composite-i.e.-smooth-curves-and-bootstrap-c.i.s"
id="toc-composite-i.e.-smooth-curves-and-bootstrap-c.i.s">4 Composite
(i.e. smooth) curves and bootstrap C.I.’s</a></li>
</ul></li>
</ul>
</div>
<div id="introduction" class="section level1">
<h1>Introduction</h1>
<p>This is a set of web pages that describe the development of a
composite curve of charcoal data drawn from the Global Charcoal Database
version 3, (GCDv3) using a set of R scripts. The intention here is to
explicitly document the analysis steps that were developed originally as
a set of Fortran programs, and which are now implemented in the R
<code>paleofire</code> package. The R scripts described here can also be
used as a point of departure for the development of new analysis
approaches.</p>
<p>The data source for these examples is a Microsoft Access
(<code>.mdb</code>) database, downloaded from <a
href="http://www.gpwg.paleofire.org/">[http://www.gpwg.paleofire.org/]</a>,
e.g., <code>GCDv03_Marlon_et_al_2015.mdb</code>. In the example here,
the scripts aim to reproduce the “Globe” curve in Fig. 6 of Marlon et
al. (2016).</p>
</div>
<div id="data" class="section level1">
<h1>Data</h1>
<p>The data used in this example are contained in two queries, saved as
“database” views or internal tables in the Microsoft Access database
named <code>GCDv03_Marlon_et_al_2015.mdb</code>, downloadable from the
Global Charcoal Database <a
href="http://paleofire.org/">[http://paleofire.org/]</a> by exporting
the full database. The queries are named (for historical reasons)
<code>ALL_BART_SITES</code> and <code>ALL_BART_DATA</code> and reside in
the Access database as “view”. <code>ALL_BART_SITES</code> contains a
list of sites, their names and locations, the depositional environment,
and the units of measurement (i.e. influx, concentration, etc.) while
<code>ALL_BART_DATA</code> contains the id, age, depth and quantity of
charcoal in each sample.</p>
<p>For the examples here, the following folder structure for the data
was used:</p>
<pre><code> /Projects/GPWG/GPWGv3/GCDv3Data/v3i/
v3i_curves/
v3i_debug/
v3i_mdb/
v3i_presamp_csv/
v3i_query/
v3i_sitelists/
v3i_sites_csv/
v3i_stats/
v3i_trans_csv/</code></pre>
<p>The the root folder and <code>v3i-mdb/</code> (into which the
database should be copied) are created by the user, and the others are
created during the analyses.</p>
</div>
<div id="analysis-steps" class="section level1">
<h1>Analysis steps</h1>
<p>There are four steps in the analysis:</p>
<ol style="list-style-type: decimal">
<li>reading the query results from the data base and making individual
“site” .csv files</li>
<li>transforming and standardizing or normalizing (i.e. converting to
anomalies) the individual records</li>
<li>implementing the presampling/prebinning step</li>
<li>composite-curve fitting using the R locfit() function, or via
binning, and estimating uncertainties via bootstrapping</li>
</ol>
<div id="query-and-site-.csv-files" class="section level2">
<h2>1 Query and site .csv files</h2>
<p>(<code>mdb-to-csv.R</code>)</p>
<p>The first step in the analysis approach here involves examining the
two query tables, checking for obvious issues in the data for individual
sites, converting all charcoal data to both influx and concentration
values, and finally extracting individual .csv files for each site. All
of the scripts here begin by setting appropriate path and folder names.
In the example script, the Access database files are read directly using
the <code>RODBC</code> package. (Note that on Windows, compiled versions
of this package exist, and a the appropriate database drivers are built
into the operating system. On OS X, a third-party database driver must
be used, and the <code>RODBC</code> package compiled from source. There
is a separate script, <code>mdb-to-csv_osx.R</code> that illustrates
this.</p>
<p>The main part of the script loops over the individual sites that are
specified in the site query, and does various checks and calculations,
including</p>
<ul>
<li>calculation of sedimentation rates and deposition times</li>
<li>checking for age or depth reversals, or other data issues</li>
<li>calculation of alternative quantities (e.g. influx, given
concentrations)</li>
<li>writing out a .csv file for each site</li>
</ul>
<p>The calculation of sedimentation rates and deposition times is
required for the conversion of concentration values to influx values and
vice-versa. Various checks for age reversals, zero sedimentation rates,
missing data are done. Typically, when a number of sites are added to
the database, there will be issues, which are flagged by this step and
resolved. In the example, such is not the case, but the script
illustrates those checks in any case. The last part of this analysis
step involves writing out one “site data” .csv file for each site
(e.g. <code>0001_data.csv</code>), plus a single “sitelist” file
(e.g. <code>v3i_all.csv</code>), which can be edited to control the
particular selection of sites that are analyzed.</p>
<p>New data not included in the database can be added to the analysis by
creating by hand a “site data” .csv file with the same format as those
created by <code>mdb-to-csv.R</code> and adding a line to the sitelist
file.</p>
</div>
<div id="transformation-and-standardizationanomalization"
class="section level2">
<h2>2 Transformation and standardization/anomalization</h2>
<p>(<code>trans-and-zscore.R</code> &
<code>trans-and-norman.R</code>)</p>
<p>Charcoal data are reported in units that range over thirteen orders
of magnitude, and charcoal records typically have “long-tailed”
distributions (Power et al., 2010). In order to compare or combine
records, the data must therefore be transformed to approach normality
(to reduce the impacts of non-constant variance) and rescaled to some
common basis or range. In one example here
(<code>trans-and-zcore.R</code>), we apply the variance-stabilzing
Box-Cox transformation, and rescale the data to “z-scores”. (For
historical reasons, the transformed data are also rescaled using the
“minimax” transformation so that all values lie between 0 and 1. This
reduces astonishment over transformed charcoal-influx or concentration
values that may wind up being negative after transformation.) This
approach also requires the specification of a base period or time
interval over which the transformation parameters are estimated and the
mean and standard deviation used for calculating z-scores are
calculated. Further discussion of this approach can be found in Power et
al. (2010) and Daniau et al. (2012).</p>
<p>A second example (<code>trans-and-norman.R</code>), illustrates the
use of “normalized” anomalies, in which the deviations of the
transformed charcoal influx values from a base period mean value are
divided by that mean value, to produce a relative deviation, scaled by
the overall level of the data. This approach is useful for
last-millennium type analyses, where records with few samples can
produce standard deviations that are not robust, and hence z-scores that
vary dramatically.</p>
<p>The specific tasks implemented by the script include, for each
site:</p>
<ul>
<li>censoring of samples with missing ages or ages after 2020 CE</li>
<li>maximum likelihood estimation of of the Box-Cox transformation
parameter <code>lambda</code></li>
<li>Box-Cox transformation of data</li>
<li>minimax rescaling of the transformed data<code>tall</code></li>
<li>calculation z-scores <code>ztrans</code> or normalized anomalies
<code>normans</code></li>
<li>writing out the transformed data for this site as a .csv file.</li>
</ul>
</div>
<div id="presamplingprebinning" class="section level2">
<h2>3 Presampling/prebinning</h2>
<p>(<code>presample-bin.R</code>)</p>
<p>Charcoal data are available at all kinds of “native” resolutions,
from samples that represent decades or centuries (or longer) to those
that represent annual deposition. Further, some records have been
interpolated to pseudo-annual time steps. In developing composite
curves, those records with higher resolutions will contribute
disproportionately to the curve. There are two general approaches for
dealing with this: 1) weighting individual charcoal (influx or
concentration) values according to their resolution, with
lower-resolution records receiving higher weights, and vice-versa, or 2)
reducing the sampling frequency of the records to some common interval
(without interpolating or creating pseudo data). We adopted the latter
approach for its simplicity and transparency.</p>
<p>The binning is done by establishing a set of evenly spaced target
points or bins, and then for each charcoal record, binning the
individual observations. If more that one observation falls in the same
bin, the average (of he transformed and standardized data) is taken as
the binned value. No effort is made to interpolate between observations,
to avoid pseudo-replication. A .csv file is written out for each
site.</p>
</div>
<div id="composite-i.e.-smooth-curves-and-bootstrap-c.i.s"
class="section level2">
<h2>4 Composite (i.e. smooth) curves and bootstrap C.I.’s</h2>
<p>(<code>smooth-curve.R</code> & <code>bin-boot.R</code>)</p>
<p>The first script (<code>smooth-curve.R</code>) uses
<code>locfit()</code> to get a (smooth) composite curve of the
(presampled/binned) charcoal z-scores or normans for a set of sites
specified by an input “sitelist” (ultimately based on all or a subset of
the sites listed in the <code>ALL_BART_SITES</code> query). The
smoothness of the curve is determined by the width of the smoothing
window, customarily specified by the “half-width” (<code>hw</code>).
First, a “global” curve (in the sense of using all of the data from a
particular list of sites is determined, and the number of sites with
samples (<code>ndec_tot</code>, for historical reasons) and the number
of samples that contribute to each fitted value
(<code>ninwin_tot</code>) are also calculated.</p>
<p>Then, over <code>nreps</code> replications, the data are sampled by
site (with replacement) to calculate bootstrap confidence intervals, and
the upper and lower 95th-percentile confidence intervals are determined.
In the example here, the curves produced by individual bootstrap samples
are plotted (in transparent gray), and the “global” curve is overplotted
in red to give a visual indication of the uncertainty in the composite
curve arising from the particular sample of sites.</p>
<p>The second script (<code>bin-boot.R</code>) creates a composite
“curve” by directly binning each charcoal influx value in
non-overlapping bins, and then calculating a simple average of the
values in each bin. This approach can be used over the past few
millennia, where the median sample density is generally less than 20
years, with an appropriate bin width, also around 20 years. This
approach yields a composite curve that is more temporally variable than
that provided by the local regression approach.</p>
</div>
</div>
</div>
<script>
// add bootstrap table styles to pandoc tables
function bootstrapStylePandocTables() {
$('tr.odd').parent('tbody').parent('table').addClass('table table-condensed');
}
$(document).ready(function () {
bootstrapStylePandocTables();
});
</script>
<!-- tabsets -->
<script>
$(document).ready(function () {
window.buildTabsets("TOC");
});
$(document).ready(function () {
$('.tabset-dropdown > .nav-tabs > li').click(function () {
$(this).parent().toggleClass('nav-tabs-open');
});
});
</script>
<!-- code folding -->
<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
(function () {
var script = document.createElement("script");
script.type = "text/javascript";
script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
document.getElementsByTagName("head")[0].appendChild(script);
})();
</script>
</body>
</html>