Dominance Analysis with statsample¶

This example demonstrates dominance analysis with the Statsample::DominanceAnalysis class

In [1]:
require 'statsample'

Statsample::Analysis.store(Statsample::DominanceAnalysis) do
sample=300
a = rnorm(sample)
b = rnorm(sample)
c = rnorm(sample)
d = rnorm(sample)

ds = Daru::DataFrame.new({:a => a,:b => b,:cc => c,:d => d})
attach(ds)
ds[:y]=a*5 + b*3 + cc*2 + d + rnorm(300)
cm=cor(ds)
summary(cm)
lr=lr(ds,:y)
summary(lr)
da=dominance_analysis(ds,:y)
summary(da)

da = dominance_analysis(ds,:y,:name=>"Dominance Analysis using group of predictors", :predictors=>[:a, :b, [:cc, :d]])
summary(da)
end

Statsample::Analysis.run_batch

Analysis 2016-03-24 15:59:53 +0000
= Statsample::DominanceAnalysis
Correlation Matrix
+----+-------+-------+-------+-------+-------+
|    |   a   |   b   |  cc   |   d   |   y   |
+----+-------+-------+-------+-------+-------+
| a  | 1.000 | .091  | .034  | -.035 | .790  |
| b  | .091  | 1.000 | .009  | .044  | .554  |
| cc | .034  | .009  | 1.000 | -.003 | .335  |
| d  | -.035 | .044  | -.003 | 1.000 | .151  |
| y  | .790  | .554  | .335  | .151  | 1.000 |
+----+-------+-------+-------+-------+-------+

== Multiple reggresion of a,b,cc,d on y
Engine: Statsample::Regression::Multiple::RubyEngine
Cases(listwise)=300(300)
R=0.988
R^2=0.977
Std.Error R=1.016
Equation=-0.124 + 5.076a + 3.002b + 1.942cc + 1.021d
=== ANOVA
ANOVA Table
+------------+-----------+-----+----------+----------+-------+
|   source   |    ss     | df  |    ms    |    f     |   p   |
+------------+-----------+-----+----------+----------+-------+
| Regression | 12860.902 | 4   | 3215.226 | 3115.863 | 0.000 |
| Error      | 304.407   | 295 | 1.032    |          |       |
| Total      | 13165.310 | 299 | 3216.257 |          |       |
+------------+-----------+-----+----------+----------+-------+

Beta coefficients
+----------+--------+-------+-------+--------+
|  coeff   |   b    | beta  |  se   |   t    |
+----------+--------+-------+-------+--------+
| Constant | -0.124 | -     | 0.059 | -2.109 |
| a        | 5.076  | 0.742 | 0.061 | 83.351 |
| b        | 3.002  | 0.477 | 0.056 | 53.594 |
| cc       | 1.942  | 0.306 | 0.056 | 34.591 |
| d        | 1.021  | 0.157 | 0.058 | 17.703 |
+----------+--------+-------+-------+--------+

== Dominance Analysis:  a,b,cc,d over y
Dominance Analysis result
+------------------+-------+-------+-------+-------+-------+-------+
|                  |  r2   | sign  |   a   |   b   |  cc   |   d   |
+------------------+-------+-------+-------+-------+-------+-------+
| Model 0          |       |       | 0.624 | 0.307 | 0.112 | 0.023 |
+------------------+-------+-------+-------+-------+-------+-------+
| a                | 0.624 | 0.000 | --    | 0.235 | 0.095 | 0.032 |
| b                | 0.307 | 0.000 | 0.552 | --    | 0.109 | 0.016 |
| cc               | 0.112 | 0.000 | 0.607 | 0.303 | --    | 0.023 |
| d                | 0.023 | 0.009 | 0.633 | 0.300 | 0.113 | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=1 Average      |       |       | 0.597 | 0.279 | 0.106 | 0.024 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b              | 0.859 | 0.000 | --    | --    | 0.094 | 0.024 |
| a*cc             | 0.720 | 0.000 | --    | 0.233 | --    | 0.032 |
| a*d              | 0.656 | 0.000 | --    | 0.227 | 0.096 | --    |
| b*cc             | 0.416 | 0.000 | 0.536 | --    | --    | 0.016 |
| b*d              | 0.323 | 0.000 | 0.560 | --    | 0.109 | --    |
| cc*d             | 0.136 | 0.000 | 0.616 | 0.297 | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=2 Average      |       |       | 0.571 | 0.252 | 0.100 | 0.024 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b*cc           | 0.952 | 0.000 | --    | --    | --    | 0.025 |
| a*b*d            | 0.883 | 0.000 | --    | --    | 0.094 | --    |
| a*cc*d           | 0.752 | 0.000 | --    | 0.225 | --    | --    |
| b*cc*d           | 0.432 | 0.000 | 0.545 | --    | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=3 Average      |       |       | 0.545 | 0.225 | 0.094 | 0.025 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b*cc*d         | 0.977 | 0.000 | --    | --    | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| Overall averages |       |       | 0.584 | 0.266 | 0.103 | 0.024 |
+------------------+-------+-------+-------+-------+-------+-------+

Pairwise dominance
+--------+-------+-------------+---------+
| Pairs  | Total | Conditional | General |
+--------+-------+-------------+---------+
| a - b  | 1.0   | 1.0         | 1.0     |
| a - cc | 1.0   | 1.0         | 1.0     |
| a - d  | 1.0   | 1.0         | 1.0     |
| b - cc | 1.0   | 1.0         | 1.0     |
| b - d  | 1.0   | 1.0         | 1.0     |
| cc - d | 1.0   | 1.0         | 1.0     |
+--------+-------+-------------+---------+

== Dominance Analysis using group of predictors
Dominance Analysis result
+------------------+-------+-------+-------+-------+--------+
|                  |  r2   | sign  |   a   |   b   | (cc,d) |
+------------------+-------+-------+-------+-------+--------+
| Model 0          |       |       | 0.624 | 0.307 | 0.136  |
+------------------+-------+-------+-------+-------+--------+
| a                | 0.624 | 0.000 | --    | 0.235 | 0.128  |
| b                | 0.307 | 0.000 | 0.552 | --    | 0.125  |
| (cc,d)           | 0.136 | 0.000 | 0.616 | 0.297 | --     |
+------------------+-------+-------+-------+-------+--------+
| k=1 Average      |       |       | 0.584 | 0.266 | 0.127  |
+------------------+-------+-------+-------+-------+--------+
| a*b              | 0.859 | 0.000 | --    | --    | 0.118  |
| a*(cc,d)         | 0.752 | 0.000 | --    | 0.225 | --     |
| b*(cc,d)         | 0.432 | 0.000 | 0.545 | --    | --     |
+------------------+-------+-------+-------+-------+--------+
| k=2 Average      |       |       | 0.545 | 0.225 | 0.118  |
+------------------+-------+-------+-------+-------+--------+
| a*b*(cc,d)       | 0.977 | 0.000 | --    | --    | --     |
+------------------+-------+-------+-------+-------+--------+
| Overall averages |       |       | 0.584 | 0.266 | 0.127  |
+------------------+-------+-------+-------+-------+--------+

Pairwise dominance
+------------+-------+-------------+---------+
|   Pairs    | Total | Conditional | General |
+------------+-------+-------------+---------+
| a - b      | 1.0   | 1.0         | 1.0     |
| a - (cc-d) | 1.0   | 1.0         | 1.0     |
| b - (cc-d) | 1.0   | 1.0         | 1.0     |
+------------+-------+-------------+---------+



This example explains usage of the Statsample::DominanceAnalysis::Bootstrap class.

In [2]:
require 'statsample'

Statsample::Analysis.store(Statsample::DominanceAnalysis::Bootstrap) do

# Remember to call *update* after an assignment/deletion cycle if lazy_update
# is *false*.
Daru.lazy_update = true
sample=300
a=rnorm(sample)
b=rnorm(sample)
c=rnorm(sample)
d=rnorm(sample)
a.rename :a
b.rename :b
c.rename :c
d.rename :d

ds = Daru::DataFrame.new({:a => a,:b => b,:cc => c,:d => d})
attach(ds)
ds[:y1] = a*5  + b*2 + cc*2 + d*2 + rnorm(sample,0,10)
ds[:y2] = a*10 + rnorm(sample)

dab=dominance_analysis_bootstrap(ds, [:y1,:y2], :debug=>true)
dab.bootstrap(100,nil)
summary(dab)
ds2=ds[:a, :b, :cc, :d, :y1]
dab2=dominance_analysis_bootstrap(ds2, :y1, :debug=>true)
dab2.bootstrap(100,nil)
summary(dab2)
Daru.lazy_update = false
end

Statsample::Analysis.run_batch

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Analysis 2016-03-24 15:59:53 +0000
= Statsample::DominanceAnalysis
Correlation Matrix
+----+-------+-------+-------+-------+-------+
|    |   a   |   b   |  cc   |   d   |   y   |
+----+-------+-------+-------+-------+-------+
| a  | 1.000 | -.067 | -.008 | -.045 | .757  |
| b  | -.067 | 1.000 | .050  | -.035 | .464  |
| cc | -.008 | .050  | 1.000 | -.008 | .351  |
| d  | -.045 | -.035 | -.008 | 1.000 | .109  |
| y  | .757  | .464  | .351  | .109  | 1.000 |
+----+-------+-------+-------+-------+-------+

== Multiple reggresion of a,b,cc,d on y
Engine: Statsample::Regression::Multiple::RubyEngine
Cases(listwise)=300(300)
R=0.988
R^2=0.976
Std.Error R=0.986
Equation=0.018 + 5.052a + 3.066b + 2.040cc + 1.002d
=== ANOVA
ANOVA Table
+------------+-----------+-----+----------+----------+-------+
|   source   |    ss     | df  |    ms    |    f     |   p   |
+------------+-----------+-----+----------+----------+-------+
| Regression | 11512.133 | 4   | 2878.033 | 2957.730 | 0.000 |
| Error      | 287.051   | 295 | 0.973    |          |       |
| Total      | 11799.185 | 299 | 2879.006 |          |       |
+------------+-----------+-----+----------+----------+-------+

Beta coefficients
+----------+-------+-------+-------+--------+
|  coeff   |   b   | beta  |  se   |   t    |
+----------+-------+-------+-------+--------+
| Constant | 0.018 | -     | 0.057 | 0.313  |
| a        | 5.052 | 0.801 | 0.057 | 87.893 |
| b        | 3.066 | 0.506 | 0.055 | 55.509 |
| cc       | 2.040 | 0.333 | 0.056 | 36.643 |
| d        | 1.002 | 0.165 | 0.055 | 18.150 |
+----------+-------+-------+-------+--------+

== Dominance Analysis:  a,b,cc,d over y
Dominance Analysis result
+------------------+-------+-------+-------+-------+-------+-------+
|                  |  r2   | sign  |   a   |   b   |  cc   |   d   |
+------------------+-------+-------+-------+-------+-------+-------+
| Model 0          |       |       | 0.573 | 0.215 | 0.123 | 0.012 |
+------------------+-------+-------+-------+-------+-------+-------+
| a                | 0.573 | 0.000 | --    | 0.266 | 0.128 | 0.021 |
| b                | 0.215 | 0.000 | 0.623 | --    | 0.107 | 0.016 |
| cc               | 0.123 | 0.000 | 0.577 | 0.199 | --    | 0.012 |
| d                | 0.012 | 0.059 | 0.581 | 0.219 | 0.124 | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=1 Average      |       |       | 0.594 | 0.228 | 0.119 | 0.016 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b              | 0.838 | 0.000 | --    | --    | 0.110 | 0.027 |
| a*cc             | 0.700 | 0.000 | --    | 0.248 | --    | 0.021 |
| a*d              | 0.593 | 0.000 | --    | 0.272 | 0.128 | --    |
| b*cc             | 0.322 | 0.000 | 0.626 | --    | --    | 0.016 |
| b*d              | 0.231 | 0.000 | 0.634 | --    | 0.108 | --    |
| cc*d             | 0.135 | 0.000 | 0.586 | 0.203 | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=2 Average      |       |       | 0.615 | 0.241 | 0.115 | 0.021 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b*cc           | 0.949 | 0.000 | --    | --    | --    | 0.027 |
| a*b*d            | 0.865 | 0.000 | --    | --    | 0.111 | --    |
| a*cc*d           | 0.722 | 0.000 | --    | 0.254 | --    | --    |
| b*cc*d           | 0.339 | 0.000 | 0.637 | --    | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=3 Average      |       |       | 0.637 | 0.254 | 0.111 | 0.027 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b*cc*d         | 0.976 | 0.000 | --    | --    | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| Overall averages |       |       | 0.605 | 0.235 | 0.117 | 0.019 |
+------------------+-------+-------+-------+-------+-------+-------+

Pairwise dominance
+--------+-------+-------------+---------+
| Pairs  | Total | Conditional | General |
+--------+-------+-------------+---------+
| a - b  | 1.0   | 1.0         | 1.0     |
| a - cc | 1.0   | 1.0         | 1.0     |
| a - d  | 1.0   | 1.0         | 1.0     |
| b - cc | 1.0   | 1.0         | 1.0     |
| b - d  | 1.0   | 1.0         | 1.0     |
| cc - d | 1.0   | 1.0         | 1.0     |
+--------+-------+-------------+---------+

== Dominance Analysis using group of predictors
Dominance Analysis result
+------------------+-------+-------+-------+-------+--------+
|                  |  r2   | sign  |   a   |   b   | (cc,d) |
+------------------+-------+-------+-------+-------+--------+
| Model 0          |       |       | 0.573 | 0.215 | 0.135  |
+------------------+-------+-------+-------+-------+--------+
| a                | 0.573 | 0.000 | --    | 0.266 | 0.149  |
| b                | 0.215 | 0.000 | 0.623 | --    | 0.124  |
| (cc,d)           | 0.135 | 0.000 | 0.586 | 0.203 | --     |
+------------------+-------+-------+-------+-------+--------+
| k=1 Average      |       |       | 0.605 | 0.234 | 0.136  |
+------------------+-------+-------+-------+-------+--------+
| a*b              | 0.838 | 0.000 | --    | --    | 0.137  |
| a*(cc,d)         | 0.722 | 0.000 | --    | 0.254 | --     |
| b*(cc,d)         | 0.339 | 0.000 | 0.637 | --    | --     |
+------------------+-------+-------+-------+-------+--------+
| k=2 Average      |       |       | 0.637 | 0.254 | 0.137  |
+------------------+-------+-------+-------+-------+--------+
| a*b*(cc,d)       | 0.976 | 0.000 | --    | --    | --     |
+------------------+-------+-------+-------+-------+--------+
| Overall averages |       |       | 0.605 | 0.235 | 0.136  |
+------------------+-------+-------+-------+-------+--------+

Pairwise dominance
+------------+-------+-------------+---------+
|   Pairs    | Total | Conditional | General |
+------------+-------+-------------+---------+
| a - b      | 1.0   | 1.0         | 1.0     |
| a - (cc-d) | 1.0   | 1.0         | 1.0     |
| b - (cc-d) | 1.0   | 1.0         | 1.0     |
+------------+-------+-------------+---------+

= Statsample::DominanceAnalysis::Bootstrap
== Bootstrap dominance Analysis:  a,b,cc,d,y1,y2 over [:y1, :y2]
Sample size: 100

t: 1.9842169515864176

Linear Regression Engine: Statsample::Regression::Multiple::MultipleDependent
Bootstrap report
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
|         pairs         | sD  |  Dij   | SE(Dij) |  Pij  |  Pji  |  Pno  | Reproducibility |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| Complete dominance    |     |        |         |       |       |       |                 |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| a - b                 | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| a - c                 | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| a - d                 | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| b - c                 | 0.0 | 0.0700 | 0.225   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - d                 | 0.0 | 0.3800 | 0.383   | 0.000 | 0.000 | 0.000 | 0.000           |
| c - d                 | 1.0 | 0.8650 | 0.292   | 0.000 | 0.000 | 0.000 | 0.000           |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| Conditional dominance |     |        |         |       |       |       |                 |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| a - b                 | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| a - c                 | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| a - d                 | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| b - c                 | 0.0 | 0.0650 | 0.221   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - d                 | 0.0 | 0.3600 | 0.390   | 0.000 | 0.000 | 0.000 | 0.000           |
| c - d                 | 1.0 | 0.8650 | 0.292   | 0.000 | 0.000 | 0.000 | 0.000           |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| General Dominance     |     |        |         |       |       |       |                 |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| a - b                 | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| a - c                 | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| a - d                 | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| b - c                 | 0.0 | 0.0500 | 0.219   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - d                 | 0.0 | 0.2600 | 0.441   | 0.000 | 0.000 | 0.000 | 0.000           |
| c - d                 | 1.0 | 0.8200 | 0.386   | 0.000 | 0.000 | 0.000 | 0.000           |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+

General averages
+-----+-------+-------+-------+-------+
| var | mean  |  se   |  p.5  | p.95  |
+-----+-------+-------+-------+-------+
| a   | 0.952 | 0.015 | 0.924 | 0.971 |
| b   | 0.005 | 0.005 | 0.001 | 0.015 |
| c   | 0.023 | 0.010 | 0.009 | 0.041 |
| d   | 0.011 | 0.009 | 0.002 | 0.030 |
+-----+-------+-------+-------+-------+

== Bootstrap dominance Analysis:  a,b,cc,d,y1 over y1
Sample size: 100

t: 1.9842169515864176

Linear Regression Engine: Statsample::Regression::Multiple::MatrixEngine
Bootstrap report
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
|         pairs         | sD  |  Dij   | SE(Dij) |  Pij  |  Pji  |  Pno  | Reproducibility |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| Complete dominance    |     |        |         |       |       |       |                 |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
|  -                    | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
|  -                    | 1.0 | 0.9800 | 0.141   | 0.000 | 0.000 | 0.000 | 0.000           |
|  -                    | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
|  -                    | 0.0 | 0.0450 | 0.175   | 0.000 | 0.000 | 0.000 | 0.000           |
|  -                    | 0.0 | 0.2850 | 0.391   | 0.000 | 0.000 | 0.000 | 0.000           |
|  -                    | 1.0 | 0.7950 | 0.356   | 0.000 | 0.000 | 0.000 | 0.000           |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| Conditional dominance |     |        |         |       |       |       |                 |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
|  -                    | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
|  -                    | 1.0 | 0.9800 | 0.141   | 0.000 | 0.000 | 0.000 | 0.000           |
|  -                    | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
|  -                    | 0.0 | 0.0400 | 0.169   | 0.000 | 0.000 | 0.000 | 0.000           |
|  -                    | 0.0 | 0.2650 | 0.399   | 0.000 | 0.000 | 0.000 | 0.000           |
|  -                    | 1.0 | 0.7950 | 0.363   | 0.000 | 0.000 | 0.000 | 0.000           |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| General Dominance     |     |        |         |       |       |       |                 |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
|  -                    | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
|  -                    | 1.0 | 0.9800 | 0.141   | 0.000 | 0.000 | 0.000 | 0.000           |
|  -                    | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
|  -                    | 0.0 | 0.0300 | 0.171   | 0.000 | 0.000 | 0.000 | 0.000           |
|  -                    | 0.0 | 0.2700 | 0.446   | 0.000 | 0.000 | 0.000 | 0.000           |
|  -                    | 1.0 | 0.7900 | 0.409   | 0.000 | 0.000 | 0.000 | 0.000           |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+

General averages
+-----+-------+-------+-------+-------+
| var | mean  |  se   |  p.5  | p.95  |
+-----+-------+-------+-------+-------+
|     | 0.182 | 0.047 | 0.103 | 0.264 |
|     | 0.007 | 0.008 | 0.000 | 0.021 |
|     | 0.039 | 0.022 | 0.012 | 0.081 |
|     | 0.017 | 0.014 | 0.001 | 0.043 |
+-----+-------+-------+-------+-------+