Dominance Analysis with statsample

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

In [2]:
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 2015-06-03 15:49:07 +0530
= Statsample::DominanceAnalysis
  Correlation Matrix
+----+-------+-------+-------+-------+-------+
|    |   a   |   b   |  cc   |   d   |   y   |
+----+-------+-------+-------+-------+-------+
| a  | 1.000 | .071  | -.013 | -.037 | .785  |
| b  | .071  | 1.000 | .046  | .011  | .545  |
| cc | -.013 | .046  | 1.000 | .061  | .322  |
| d  | -.037 | .011  | .061  | 1.000 | .154  |
| y  | .785  | .545  | .322  | .154  | 1.000 |
+----+-------+-------+-------+-------+-------+

  == Multiple reggresion of a,b,cc,d on y
    Engine: Statsample::Regression::Multiple::RubyEngine
    Cases(listwise)=300(300)
    R=0.989
    R^2=0.978
    R^2 Adj=0.977
    Std.Error R=0.984
    Equation=-0.062 + 5.000a + 2.986b + 2.004cc + 1.046d
    === ANOVA
      ANOVA Table
+------------+-----------+-----+----------+----------+-------+
|   source   |    ss     | df  |    ms    |    f     |   p   |
+------------+-----------+-----+----------+----------+-------+
| Regression | 12431.643 | 4   | 3107.911 | 3211.058 | 0.000 |
| Error      | 285.524   | 295 | 0.968    |          |       |
| Total      | 12717.167 | 299 | 3108.879 |          |       |
+------------+-----------+-----+----------+----------+-------+

    Beta coefficients
+----------+--------+-------+-------+--------+
|  coeff   |   b    | beta  |  se   |   t    |
+----------+--------+-------+-------+--------+
| Constant | -0.062 | -     | 0.057 | -1.080 |
| a        | 5.000  | 0.761 | 0.058 | 86.894 |
| b        | 2.986  | 0.476 | 0.055 | 54.325 |
| cc       | 2.004  | 0.300 | 0.058 | 34.323 |
| d        | 1.046  | 0.159 | 0.058 | 18.180 |
+----------+--------+-------+-------+--------+

  == Dominance Analysis:  a,b,cc,d over y
    Dominance Analysis result
+------------------+-------+-------+-------+-------+-------+-------+
|                  |  r2   | sign  |   a   |   b   |  cc   |   d   |
+------------------+-------+-------+-------+-------+-------+-------+
| Model 0          |       |       | 0.616 | 0.297 | 0.104 | 0.024 |
+------------------+-------+-------+-------+-------+-------+-------+
| a                | 0.616 | 0.000 | --    | 0.241 | 0.110 | 0.034 |
| b                | 0.297 | 0.000 | 0.559 | --    | 0.088 | 0.022 |
| cc               | 0.104 | 0.000 | 0.622 | 0.282 | --    | 0.018 |
| d                | 0.024 | 0.007 | 0.626 | 0.296 | 0.098 | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=1 Average      |       |       | 0.602 | 0.273 | 0.099 | 0.025 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b              | 0.857 | 0.000 | --    | --    | 0.096 | 0.031 |
| a*cc             | 0.726 | 0.000 | --    | 0.226 | --    | 0.027 |
| a*d              | 0.650 | 0.000 | --    | 0.238 | 0.103 | --    |
| b*cc             | 0.386 | 0.000 | 0.566 | --    | --    | 0.017 |
| b*d              | 0.319 | 0.000 | 0.568 | --    | 0.083 | --    |
| cc*d             | 0.122 | 0.000 | 0.631 | 0.281 | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=2 Average      |       |       | 0.589 | 0.249 | 0.094 | 0.025 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b*cc           | 0.952 | 0.000 | --    | --    | --    | 0.025 |
| a*b*d            | 0.888 | 0.000 | --    | --    | 0.090 | --    |
| a*cc*d           | 0.753 | 0.000 | --    | 0.225 | --    | --    |
| b*cc*d           | 0.403 | 0.000 | 0.575 | --    | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=3 Average      |       |       | 0.575 | 0.225 | 0.090 | 0.025 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b*cc*d         | 0.978 | 0.000 | --    | --    | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| Overall averages |       |       | 0.595 | 0.261 | 0.097 | 0.025 |
+------------------+-------+-------+-------+-------+-------+-------+

    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          |       |       | 0.616 | 0.297 | 0.122  |
+------------------+-------+-------+-------+-------+--------+
| a                | 0.616 | 0.000 | --    | 0.241 | 0.137  |
| b                | 0.297 | 0.000 | 0.559 | --    | 0.105  |
| (cc,d)           | 0.122 | 0.000 | 0.631 | 0.281 | --     |
+------------------+-------+-------+-------+-------+--------+
| k=1 Average      |       |       | 0.595 | 0.261 | 0.121  |
+------------------+-------+-------+-------+-------+--------+
| a*b              | 0.857 | 0.000 | --    | --    | 0.121  |
| a*(cc,d)         | 0.753 | 0.000 | --    | 0.225 | --     |
| b*(cc,d)         | 0.403 | 0.000 | 0.575 | --    | --     |
+------------------+-------+-------+-------+-------+--------+
| k=2 Average      |       |       | 0.575 | 0.225 | 0.121  |
+------------------+-------+-------+-------+-------+--------+
| a*b*(cc,d)       | 0.978 | 0.000 | --    | --    | --     |
+------------------+-------+-------+-------+-------+--------+
| Overall averages |       |       | 0.595 | 0.261 | 0.121  |
+------------------+-------+-------+-------+-------+--------+

    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 [4]:
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

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Analysis 2015-06-03 16:03:14 +0530
= Statsample::DominanceAnalysis
  Correlation Matrix
+----+-------+-------+-------+-------+-------+
|    |   a   |   b   |  cc   |   d   |   y   |
+----+-------+-------+-------+-------+-------+
| a  | 1.000 | .026  | -.035 | -.090 | .784  |
| b  | .026  | 1.000 | -.051 | .169  | .493  |
| cc | -.035 | -.051 | 1.000 | .127  | .284  |
| d  | -.090 | .169  | .127  | 1.000 | .206  |
| y  | .784  | .493  | .284  | .206  | 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
    R^2 Adj=0.975
    Std.Error R=0.983
    Equation=0.030 + 4.956a + 2.876b + 1.948cc + 1.049d
    === ANOVA
      ANOVA Table
+------------+-----------+-----+----------+----------+-------+
|   source   |    ss     | df  |    ms    |    f     |   p   |
+------------+-----------+-----+----------+----------+-------+
| Regression | 11379.077 | 4   | 2844.769 | 2942.454 | 0.000 |
| Error      | 285.206   | 295 | 0.967    |          |       |
| Total      | 11664.283 | 299 | 2845.736 |          |       |
+------------+-----------+-----+----------+----------+-------+

    Beta coefficients
+----------+-------+-------+-------+--------+
|  coeff   |   b   | beta  |  se   |   t    |
+----------+-------+-------+-------+--------+
| Constant | 0.030 | -     | 0.057 | 0.520  |
| a        | 4.956 | 0.798 | 0.057 | 87.146 |
| b        | 2.876 | 0.462 | 0.058 | 49.839 |
| cc       | 1.948 | 0.316 | 0.057 | 34.280 |
| d        | 1.049 | 0.160 | 0.062 | 17.057 |
+----------+-------+-------+-------+--------+

  == Dominance Analysis:  a,b,cc,d over y
    Dominance Analysis result
+------------------+-------+-------+-------+-------+-------+-------+
|                  |  r2   | sign  |   a   |   b   |  cc   |   d   |
+------------------+-------+-------+-------+-------+-------+-------+
| Model 0          |       |       | 0.614 | 0.243 | 0.081 | 0.042 |
+------------------+-------+-------+-------+-------+-------+-------+
| a                | 0.614 | 0.000 | --    | 0.224 | 0.097 | 0.077 |
| b                | 0.243 | 0.000 | 0.595 | --    | 0.096 | 0.015 |
| cc               | 0.081 | 0.000 | 0.631 | 0.258 | --    | 0.029 |
| d                | 0.042 | 0.000 | 0.649 | 0.216 | 0.068 | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=1 Average      |       |       | 0.625 | 0.233 | 0.087 | 0.041 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b              | 0.838 | 0.000 | --    | --    | 0.113 | 0.040 |
| a*cc             | 0.712 | 0.000 | --    | 0.240 | --    | 0.058 |
| a*d              | 0.691 | 0.000 | --    | 0.187 | 0.078 | --    |
| b*cc             | 0.339 | 0.000 | 0.612 | --    | --    | 0.007 |
| b*d              | 0.259 | 0.000 | 0.619 | --    | 0.087 | --    |
| cc*d             | 0.110 | 0.000 | 0.660 | 0.236 | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=2 Average      |       |       | 0.630 | 0.221 | 0.093 | 0.035 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b*cc           | 0.951 | 0.000 | --    | --    | --    | 0.024 |
| a*b*d            | 0.878 | 0.000 | --    | --    | 0.097 | --    |
| a*cc*d           | 0.770 | 0.000 | --    | 0.206 | --    | --    |
| b*cc*d           | 0.346 | 0.000 | 0.629 | --    | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| k=3 Average      |       |       | 0.629 | 0.206 | 0.097 | 0.024 |
+------------------+-------+-------+-------+-------+-------+-------+
| a*b*cc*d         | 0.976 | 0.000 | --    | --    | --    | --    |
+------------------+-------+-------+-------+-------+-------+-------+
| Overall averages |       |       | 0.625 | 0.226 | 0.090 | 0.035 |
+------------------+-------+-------+-------+-------+-------+-------+

    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          |       |       | 0.614 | 0.243 | 0.110  |
+------------------+-------+-------+-------+-------+--------+
| a                | 0.614 | 0.000 | --    | 0.224 | 0.155  |
| b                | 0.243 | 0.000 | 0.595 | --    | 0.103  |
| (cc,d)           | 0.110 | 0.000 | 0.660 | 0.236 | --     |
+------------------+-------+-------+-------+-------+--------+
| k=1 Average      |       |       | 0.627 | 0.230 | 0.129  |
+------------------+-------+-------+-------+-------+--------+
| a*b              | 0.838 | 0.000 | --    | --    | 0.137  |
| a*(cc,d)         | 0.770 | 0.000 | --    | 0.206 | --     |
| b*(cc,d)         | 0.346 | 0.000 | 0.629 | --    | --     |
+------------------+-------+-------+-------+-------+--------+
| k=2 Average      |       |       | 0.629 | 0.206 | 0.137  |
+------------------+-------+-------+-------+-------+--------+
| a*b*(cc,d)       | 0.976 | 0.000 | --    | --    | --     |
+------------------+-------+-------+-------+-------+--------+
| Overall averages |       |       | 0.624 | 0.226 | 0.125  |
+------------------+-------+-------+-------+-------+--------+

    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: 1.9842169363295818

    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 - cc                | 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 - cc                | 0.5 | 0.4500 | 0.379   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - d                 | 1.0 | 0.5800 | 0.448   | 0.000 | 0.000 | 0.000 | 0.000           |
| cc - d                | 0.5 | 0.5800 | 0.381   | 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 - cc                | 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 - cc                | 0.5 | 0.4550 | 0.383   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - d                 | 1.0 | 0.5800 | 0.459   | 0.000 | 0.000 | 0.000 | 0.000           |
| cc - d                | 0.5 | 0.5700 | 0.389   | 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 - cc                | 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 - cc                | 1.0 | 0.6300 | 0.485   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - d                 | 1.0 | 0.5800 | 0.496   | 0.000 | 0.000 | 0.000 | 0.000           |
| cc - d                | 0.0 | 0.3800 | 0.488   | 0.000 | 0.000 | 0.000 | 0.000           |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+

    General averages
+-----+-------+-------+-------+-------+
| var | mean  |  se   |  p.5  | p.95  |
+-----+-------+-------+-------+-------+
| a   | 0.934 | 0.017 | 0.908 | 0.962 |
| b   | 0.021 | 0.010 | 0.007 | 0.042 |
| cc  | 0.016 | 0.011 | 0.003 | 0.039 |
| d   | 0.020 | 0.012 | 0.003 | 0.040 |
+-----+-------+-------+-------+-------+

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

    t: 1.9842169363295818

    Linear Regression Engine: Statsample::Regression::Multiple::MatrixEngine
    Bootstrap report
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
|         pairs         | sD  |  Dij   | SE(Dij) |  Pij  |  Pji  |  Pno  | Reproducibility |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| Complete dominance    |     |        |         |       |       |       |                 |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| a - b                 | 1.0 | 0.9950 | 0.050   | 0.000 | 0.000 | 0.000 | 0.000           |
| a - cc                | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| a - d                 | 1.0 | 0.9900 | 0.100   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - cc                | 1.0 | 0.6700 | 0.434   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - d                 | 0.5 | 0.5050 | 0.429   | 0.000 | 0.000 | 0.000 | 0.000           |
| cc - d                | 0.0 | 0.4000 | 0.426   | 0.000 | 0.000 | 0.000 | 0.000           |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| Conditional dominance |     |        |         |       |       |       |                 |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| a - b                 | 1.0 | 0.9950 | 0.050   | 0.000 | 0.000 | 0.000 | 0.000           |
| a - cc                | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| a - d                 | 1.0 | 0.9900 | 0.100   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - cc                | 1.0 | 0.6700 | 0.445   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - d                 | 0.5 | 0.5100 | 0.449   | 0.000 | 0.000 | 0.000 | 0.000           |
| cc - d                | 0.0 | 0.4000 | 0.438   | 0.000 | 0.000 | 0.000 | 0.000           |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| General Dominance     |     |        |         |       |       |       |                 |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+
| a - b                 | 1.0 | 0.9900 | 0.100   | 0.000 | 0.000 | 0.000 | 0.000           |
| a - cc                | 1.0 | 1.0000 | 0.000   | 1.000 | 0.000 | 0.000 | 1.000           |
| a - d                 | 1.0 | 0.9900 | 0.100   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - cc                | 1.0 | 0.6900 | 0.465   | 0.000 | 0.000 | 0.000 | 0.000           |
| b - d                 | 1.0 | 0.5400 | 0.501   | 0.000 | 0.000 | 0.000 | 0.000           |
| cc - d                | 0.0 | 0.3900 | 0.490   | 0.000 | 0.000 | 0.000 | 0.000           |
+-----------------------+-----+--------+---------+-------+-------+-------+-----------------+

    General averages
+-----+-------+-------+-------+-------+
| var | mean  |  se   |  p.5  | p.95  |
+-----+-------+-------+-------+-------+
| a   | 0.144 | 0.038 | 0.094 | 0.223 |
| b   | 0.030 | 0.017 | 0.010 | 0.065 |
| cc  | 0.022 | 0.016 | 0.004 | 0.049 |
| d   | 0.031 | 0.024 | 0.004 | 0.078 |
+-----+-------+-------+-------+-------+