partition: Hierarchical Partitioning from a List of Goodness of Fit...
In hier.part: Hierarchical Partitioning
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
Partitions variance in a multivariate dataset from a list of goodness
of fit measures
Usage
1
Arguments
gfs
an array as outputted by the function all.regs or a vector of
goodness of fit measures from a hierarchy of regressions based on pcan
variables in ascending order (as produced by function combos,
but also including the null model as the first element)
pcan
the number of variables from which the hierarchy was constructed
(maximum = 12)
var.names
an array of pcan variable names, if required
Details
This function applies the hierarchical partitioning algorithm of Chevan
and Sutherland (1991) to return a simple table listing of each variable,
its independent contribution (I) and its conjoint contribution with all
other variables (J). The output is identical to the function
hier.part, which takes the dependent and independent variable
data as its input.
Note earlier versions of partition (hier.part<1.0) produced a matrix and
barplot of percentage distribution of effects as a percentage of the sum
of all Is and Js, as portrayed in Hatt et al. (2004) and Walsh et al.
(2004). This version plots the percentage distribution of independent
effects only. The sum of Is equals the goodness of fit measure of the
full model minus the goodness of fit measure of the null model.
The distribution of joint effects shows the relative contribution of
each variable to shared variability in the full model. Negative joint
effects are possible for variables that act as suppressors of other
variables (Chevan and Sutherland 1991).
At this stage, the partition routine will not run for more than 12
independent variables.
Value
a list containing
gfs
a data frame listing all combinations of predictor
variables in the first column in ascending order, and the
corresponding goodness of fit measure for the model using those
variables
IJ
a data frame of I, the independent and J the joint
contribution for each predictor variable
I.perc
a data frame of I as a percentage of total explained variance
J.perc
a data frame of J as a percentage of sum of all Js
Note
The function produces a minor rounding error for hierarchies
constructed from more than 9 variables. To check if this error affects
the inference from an analysis, run the analysis several times with
the variables entered in a different order. There are no known
problems for hierarchies with 9 or fewer variables.
Author(s)
Chris Walsh cwalsh@unimelb.edu.au using c and fortran
code written by Ralph Mac Nally Ralph.MacNally@gmail.com.
References
Chevan, A. and Sutherland, M. 1991 Hierarchical Partitioning. The
American Statistician 45, 90–96.
Hatt, B. E., Fletcher, T. D., Walsh, C. J. and Taylor, S. L. 2004 The
influence of urban density and drainage infrastructure on the
concentrations and loads of pollutants in small
streams. Environmental Management 34, 112–124.
See Also
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
#linear regression of log(electrical conductivity) in streams
#against seven independent variables describing catchment
#characteristics (from Hatt et al. 2004).
data(urbanwq)
env <- urbanwq[,2:8]
gofs <- all.regs(urbanwq$lec, env, fam = "gaussian",
gof = "Rsqu", print.vars = TRUE)
partition(gofs, pcan = 7, var.names = names(urbanwq[,2,8]))
#hierarchical partitioning of logistic and linear regression
#goodness of fit measures from Chevan and Sutherland (1991).
data(chevan)
partition(chevan$chisq, pcan = 4)
partition(chevan$rsqu, pcan = 4)
Example output
Loading required package: gtools
regressions done: formatting results
$gfs
variable.combination gof
1 Theta 0.00000000
2 fimp 0.59047318
3 sconn 0.82682075
4 sdensep 0.01098174
5 unsealden 0.39635905
6 fcarea 0.12282709
7 selev 0.62445471
8 amgeast 0.33033972
9 fimp sconn 0.83410378
10 fimp sdensep 0.59758915
11 fimp unsealden 0.62061433
12 fimp fcarea 0.65284362
13 fimp selev 0.77159448
14 fimp amgeast 0.60702109
15 sconn sdensep 0.82683793
16 sconn unsealden 0.82691037
17 sconn fcarea 0.83582029
18 sconn selev 0.85403927
19 sconn amgeast 0.84727070
20 sdensep unsealden 0.41798147
21 sdensep fcarea 0.13980912
22 sdensep selev 0.76026824
23 sdensep amgeast 0.33080645
24 unsealden fcarea 0.39744819
25 unsealden selev 0.66503431
26 unsealden amgeast 0.52650125
27 fcarea selev 0.67608730
28 fcarea amgeast 0.43330271
29 selev amgeast 0.64633406
30 fimp sconn sdensep 0.83447868
31 fimp sconn unsealden 0.83411192
32 fimp sconn fcarea 0.83965414
33 fimp sconn selev 0.85551898
34 fimp sconn amgeast 0.84727151
35 fimp sdensep unsealden 0.62061622
36 fimp sdensep fcarea 0.65949970
37 fimp sdensep selev 0.82672399
38 fimp sdensep amgeast 0.62672410
39 fimp unsealden fcarea 0.65445206
40 fimp unsealden selev 0.77226833
41 fimp unsealden amgeast 0.62512912
42 fimp fcarea selev 0.77811174
43 fimp fcarea amgeast 0.66312305
44 fimp selev amgeast 0.82026934
45 sconn sdensep unsealden 0.82691040
46 sconn sdensep fcarea 0.84141253
47 sconn sdensep selev 0.87751308
48 sconn sdensep amgeast 0.84785650
49 sconn unsealden fcarea 0.83932285
50 sconn unsealden selev 0.85513956
51 sconn unsealden amgeast 0.84985538
52 sconn fcarea selev 0.85490360
53 sconn fcarea amgeast 0.85107746
54 sconn selev amgeast 0.87685251
55 sdensep unsealden fcarea 0.43348171
56 sdensep unsealden selev 0.81801707
57 sdensep unsealden amgeast 0.55827372
58 sdensep fcarea selev 0.76851361
59 sdensep fcarea amgeast 0.50536622
60 sdensep selev amgeast 0.77107209
61 unsealden fcarea selev 0.73969961
62 unsealden fcarea amgeast 0.53654123
63 unsealden selev amgeast 0.68316625
64 fcarea selev amgeast 0.67713148
65 fimp sconn sdensep unsealden 0.83451931
66 fimp sconn sdensep fcarea 0.84541929
67 fimp sconn sdensep selev 0.87865868
68 fimp sconn sdensep amgeast 0.84793008
69 fimp sconn unsealden fcarea 0.84176310
70 fimp sconn unsealden selev 0.85633390
71 fimp sconn unsealden amgeast 0.85010056
72 fimp sconn fcarea selev 0.85662169
73 fimp sconn fcarea amgeast 0.85116200
74 fimp sconn selev amgeast 0.88236321
75 fimp sdensep unsealden fcarea 0.66297682
76 fimp sdensep unsealden selev 0.84039075
77 fimp sdensep unsealden amgeast 0.62908864
78 fimp sdensep fcarea selev 0.82701685
79 fimp sdensep fcarea amgeast 0.66414800
80 fimp sdensep selev amgeast 0.85116957
81 fimp unsealden fcarea selev 0.78348135
82 fimp unsealden fcarea amgeast 0.66312339
83 fimp unsealden selev amgeast 0.82956916
84 fimp fcarea selev amgeast 0.85200153
85 sconn sdensep unsealden fcarea 0.84338543
86 sconn sdensep unsealden selev 0.87900342
87 sconn sdensep unsealden amgeast 0.85317612
88 sconn sdensep fcarea selev 0.87755498
89 sconn sdensep fcarea amgeast 0.85162358
90 sconn sdensep selev amgeast 0.89200389
91 sconn unsealden fcarea selev 0.85535421
92 sconn unsealden fcarea amgeast 0.85816222
93 sconn unsealden selev amgeast 0.88318976
94 sconn fcarea selev amgeast 0.88611089
95 sdensep unsealden fcarea selev 0.83628377
96 sdensep unsealden fcarea amgeast 0.61132790
97 sdensep unsealden selev amgeast 0.82521005
98 sdensep fcarea selev amgeast 0.77285776
99 unsealden fcarea selev amgeast 0.74013871
100 fimp sconn sdensep unsealden fcarea 0.84631087
101 fimp sconn sdensep unsealden selev 0.88052535
102 fimp sconn sdensep unsealden amgeast 0.85779318
103 fimp sconn sdensep fcarea selev 0.87866729
104 fimp sconn sdensep fcarea amgeast 0.85162457
105 fimp sconn sdensep selev amgeast 0.89525987
106 fimp sconn unsealden fcarea selev 0.85679323
107 fimp sconn unsealden fcarea amgeast 0.86058475
108 fimp sconn unsealden selev amgeast 0.89708584
109 fimp sconn fcarea selev amgeast 0.89557323
110 fimp sdensep unsealden fcarea selev 0.84575908
111 fimp sdensep unsealden fcarea amgeast 0.66461591
112 fimp sdensep unsealden selev amgeast 0.85137732
113 fimp sdensep fcarea selev amgeast 0.86367597
114 fimp unsealden fcarea selev amgeast 0.85322499
115 sconn sdensep unsealden fcarea selev 0.87916623
116 sconn sdensep unsealden fcarea amgeast 0.85818567
117 sconn sdensep unsealden selev amgeast 0.89224695
118 sconn sdensep fcarea selev amgeast 0.89515882
119 sconn unsealden fcarea selev amgeast 0.88779139
120 sdensep unsealden fcarea selev amgeast 0.83642968
121 fimp sconn sdensep unsealden fcarea selev 0.88093891
122 fimp sconn sdensep unsealden fcarea amgeast 0.86223879
123 fimp sconn sdensep unsealden selev amgeast 0.89900950
124 fimp sconn sdensep fcarea selev amgeast 0.90101494
125 fimp sconn unsealden fcarea selev amgeast 0.90231612
126 fimp sdensep unsealden fcarea selev amgeast 0.86447417
127 sconn sdensep unsealden fcarea selev amgeast 0.89516613
128 fimp sconn sdensep unsealden fcarea selev amgeast 0.90324171
$IJ
I J Total
1 0.16018583 0.430287348 0.59047318
2 0.28970489 0.537115864 0.82682075
3 0.02090086 -0.009919125 0.01098174
4 0.09181298 0.304546072 0.39635905
5 0.03609565 0.086731439 0.12282709
6 0.21589289 0.408561821 0.62445471
7 0.08864861 0.241691110 0.33033972
$I.perc
I
1 17.734548
2 32.073905
3 2.313983
4 10.164829
5 3.996234
6 23.902006
7 9.814495
$gfs
[1] 207.5 191.6 113.8 68.5 185.5 104.4 58.6 173.3 27.7 104.8 53.4 20.2
[13] 97.0 46.3 19.3 13.6
$IJ
I J Total
1 -9.891667 -6.008333 -15.9
2 -61.391667 -32.308333 -93.7
3 -109.591667 -29.408333 -139.0
4 -13.025000 -8.975000 -22.0
$I.perc
I
1 5.101427
2 31.661509
3 56.519684
4 6.717380
$gfs
[1] 0.000 0.010 0.060 0.086 0.014 0.065 0.090 0.022 0.107 0.065 0.094 0.110
[13] 0.070 0.097 0.111 0.114
$IJ
I J Total
1 0.005583333 0.004416667 0.010
2 0.036916667 0.023083333 0.060
3 0.063583333 0.022416667 0.086
4 0.007916667 0.006083333 0.014
$I.perc
I
1 4.897661
2 32.383041
3 55.774854
4 6.944444
hier.part documentation built on March 3, 2020, 9:07 a.m.
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
Partitions variance in a multivariate dataset from a list of goodness of fit measures
Usage
1 |
Arguments
gfs |
an array as outputted by the function |
pcan |
the number of variables from which the hierarchy was constructed (maximum = 12) |
var.names |
an array of pcan variable names, if required |
Details
This function applies the hierarchical partitioning algorithm of Chevan
and Sutherland (1991) to return a simple table listing of each variable,
its independent contribution (I) and its conjoint contribution with all
other variables (J). The output is identical to the function
hier.part, which takes the dependent and independent variable
data as its input.
Note earlier versions of partition (hier.part<1.0) produced a matrix and barplot of percentage distribution of effects as a percentage of the sum of all Is and Js, as portrayed in Hatt et al. (2004) and Walsh et al. (2004). This version plots the percentage distribution of independent effects only. The sum of Is equals the goodness of fit measure of the full model minus the goodness of fit measure of the null model.
The distribution of joint effects shows the relative contribution of each variable to shared variability in the full model. Negative joint effects are possible for variables that act as suppressors of other variables (Chevan and Sutherland 1991).
At this stage, the partition routine will not run for more than 12 independent variables.
Value
a list containing
gfs |
a data frame listing all combinations of predictor variables in the first column in ascending order, and the corresponding goodness of fit measure for the model using those variables |
IJ |
a data frame of I, the independent and J the joint contribution for each predictor variable |
I.perc |
a data frame of I as a percentage of total explained variance |
J.perc |
a data frame of J as a percentage of sum of all Js |
Note
The function produces a minor rounding error for hierarchies constructed from more than 9 variables. To check if this error affects the inference from an analysis, run the analysis several times with the variables entered in a different order. There are no known problems for hierarchies with 9 or fewer variables.
Author(s)
Chris Walsh cwalsh@unimelb.edu.au using c and fortran code written by Ralph Mac Nally Ralph.MacNally@gmail.com.
References
Chevan, A. and Sutherland, M. 1991 Hierarchical Partitioning. The American Statistician 45, 90–96.
Hatt, B. E., Fletcher, T. D., Walsh, C. J. and Taylor, S. L. 2004 The influence of urban density and drainage infrastructure on the concentrations and loads of pollutants in small streams. Environmental Management 34, 112–124.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | #linear regression of log(electrical conductivity) in streams
#against seven independent variables describing catchment
#characteristics (from Hatt et al. 2004).
data(urbanwq)
env <- urbanwq[,2:8]
gofs <- all.regs(urbanwq$lec, env, fam = "gaussian",
gof = "Rsqu", print.vars = TRUE)
partition(gofs, pcan = 7, var.names = names(urbanwq[,2,8]))
#hierarchical partitioning of logistic and linear regression
#goodness of fit measures from Chevan and Sutherland (1991).
data(chevan)
partition(chevan$chisq, pcan = 4)
partition(chevan$rsqu, pcan = 4)
|
Example output
Loading required package: gtools
regressions done: formatting results
$gfs
variable.combination gof
1 Theta 0.00000000
2 fimp 0.59047318
3 sconn 0.82682075
4 sdensep 0.01098174
5 unsealden 0.39635905
6 fcarea 0.12282709
7 selev 0.62445471
8 amgeast 0.33033972
9 fimp sconn 0.83410378
10 fimp sdensep 0.59758915
11 fimp unsealden 0.62061433
12 fimp fcarea 0.65284362
13 fimp selev 0.77159448
14 fimp amgeast 0.60702109
15 sconn sdensep 0.82683793
16 sconn unsealden 0.82691037
17 sconn fcarea 0.83582029
18 sconn selev 0.85403927
19 sconn amgeast 0.84727070
20 sdensep unsealden 0.41798147
21 sdensep fcarea 0.13980912
22 sdensep selev 0.76026824
23 sdensep amgeast 0.33080645
24 unsealden fcarea 0.39744819
25 unsealden selev 0.66503431
26 unsealden amgeast 0.52650125
27 fcarea selev 0.67608730
28 fcarea amgeast 0.43330271
29 selev amgeast 0.64633406
30 fimp sconn sdensep 0.83447868
31 fimp sconn unsealden 0.83411192
32 fimp sconn fcarea 0.83965414
33 fimp sconn selev 0.85551898
34 fimp sconn amgeast 0.84727151
35 fimp sdensep unsealden 0.62061622
36 fimp sdensep fcarea 0.65949970
37 fimp sdensep selev 0.82672399
38 fimp sdensep amgeast 0.62672410
39 fimp unsealden fcarea 0.65445206
40 fimp unsealden selev 0.77226833
41 fimp unsealden amgeast 0.62512912
42 fimp fcarea selev 0.77811174
43 fimp fcarea amgeast 0.66312305
44 fimp selev amgeast 0.82026934
45 sconn sdensep unsealden 0.82691040
46 sconn sdensep fcarea 0.84141253
47 sconn sdensep selev 0.87751308
48 sconn sdensep amgeast 0.84785650
49 sconn unsealden fcarea 0.83932285
50 sconn unsealden selev 0.85513956
51 sconn unsealden amgeast 0.84985538
52 sconn fcarea selev 0.85490360
53 sconn fcarea amgeast 0.85107746
54 sconn selev amgeast 0.87685251
55 sdensep unsealden fcarea 0.43348171
56 sdensep unsealden selev 0.81801707
57 sdensep unsealden amgeast 0.55827372
58 sdensep fcarea selev 0.76851361
59 sdensep fcarea amgeast 0.50536622
60 sdensep selev amgeast 0.77107209
61 unsealden fcarea selev 0.73969961
62 unsealden fcarea amgeast 0.53654123
63 unsealden selev amgeast 0.68316625
64 fcarea selev amgeast 0.67713148
65 fimp sconn sdensep unsealden 0.83451931
66 fimp sconn sdensep fcarea 0.84541929
67 fimp sconn sdensep selev 0.87865868
68 fimp sconn sdensep amgeast 0.84793008
69 fimp sconn unsealden fcarea 0.84176310
70 fimp sconn unsealden selev 0.85633390
71 fimp sconn unsealden amgeast 0.85010056
72 fimp sconn fcarea selev 0.85662169
73 fimp sconn fcarea amgeast 0.85116200
74 fimp sconn selev amgeast 0.88236321
75 fimp sdensep unsealden fcarea 0.66297682
76 fimp sdensep unsealden selev 0.84039075
77 fimp sdensep unsealden amgeast 0.62908864
78 fimp sdensep fcarea selev 0.82701685
79 fimp sdensep fcarea amgeast 0.66414800
80 fimp sdensep selev amgeast 0.85116957
81 fimp unsealden fcarea selev 0.78348135
82 fimp unsealden fcarea amgeast 0.66312339
83 fimp unsealden selev amgeast 0.82956916
84 fimp fcarea selev amgeast 0.85200153
85 sconn sdensep unsealden fcarea 0.84338543
86 sconn sdensep unsealden selev 0.87900342
87 sconn sdensep unsealden amgeast 0.85317612
88 sconn sdensep fcarea selev 0.87755498
89 sconn sdensep fcarea amgeast 0.85162358
90 sconn sdensep selev amgeast 0.89200389
91 sconn unsealden fcarea selev 0.85535421
92 sconn unsealden fcarea amgeast 0.85816222
93 sconn unsealden selev amgeast 0.88318976
94 sconn fcarea selev amgeast 0.88611089
95 sdensep unsealden fcarea selev 0.83628377
96 sdensep unsealden fcarea amgeast 0.61132790
97 sdensep unsealden selev amgeast 0.82521005
98 sdensep fcarea selev amgeast 0.77285776
99 unsealden fcarea selev amgeast 0.74013871
100 fimp sconn sdensep unsealden fcarea 0.84631087
101 fimp sconn sdensep unsealden selev 0.88052535
102 fimp sconn sdensep unsealden amgeast 0.85779318
103 fimp sconn sdensep fcarea selev 0.87866729
104 fimp sconn sdensep fcarea amgeast 0.85162457
105 fimp sconn sdensep selev amgeast 0.89525987
106 fimp sconn unsealden fcarea selev 0.85679323
107 fimp sconn unsealden fcarea amgeast 0.86058475
108 fimp sconn unsealden selev amgeast 0.89708584
109 fimp sconn fcarea selev amgeast 0.89557323
110 fimp sdensep unsealden fcarea selev 0.84575908
111 fimp sdensep unsealden fcarea amgeast 0.66461591
112 fimp sdensep unsealden selev amgeast 0.85137732
113 fimp sdensep fcarea selev amgeast 0.86367597
114 fimp unsealden fcarea selev amgeast 0.85322499
115 sconn sdensep unsealden fcarea selev 0.87916623
116 sconn sdensep unsealden fcarea amgeast 0.85818567
117 sconn sdensep unsealden selev amgeast 0.89224695
118 sconn sdensep fcarea selev amgeast 0.89515882
119 sconn unsealden fcarea selev amgeast 0.88779139
120 sdensep unsealden fcarea selev amgeast 0.83642968
121 fimp sconn sdensep unsealden fcarea selev 0.88093891
122 fimp sconn sdensep unsealden fcarea amgeast 0.86223879
123 fimp sconn sdensep unsealden selev amgeast 0.89900950
124 fimp sconn sdensep fcarea selev amgeast 0.90101494
125 fimp sconn unsealden fcarea selev amgeast 0.90231612
126 fimp sdensep unsealden fcarea selev amgeast 0.86447417
127 sconn sdensep unsealden fcarea selev amgeast 0.89516613
128 fimp sconn sdensep unsealden fcarea selev amgeast 0.90324171
$IJ
I J Total
1 0.16018583 0.430287348 0.59047318
2 0.28970489 0.537115864 0.82682075
3 0.02090086 -0.009919125 0.01098174
4 0.09181298 0.304546072 0.39635905
5 0.03609565 0.086731439 0.12282709
6 0.21589289 0.408561821 0.62445471
7 0.08864861 0.241691110 0.33033972
$I.perc
I
1 17.734548
2 32.073905
3 2.313983
4 10.164829
5 3.996234
6 23.902006
7 9.814495
$gfs
[1] 207.5 191.6 113.8 68.5 185.5 104.4 58.6 173.3 27.7 104.8 53.4 20.2
[13] 97.0 46.3 19.3 13.6
$IJ
I J Total
1 -9.891667 -6.008333 -15.9
2 -61.391667 -32.308333 -93.7
3 -109.591667 -29.408333 -139.0
4 -13.025000 -8.975000 -22.0
$I.perc
I
1 5.101427
2 31.661509
3 56.519684
4 6.717380
$gfs
[1] 0.000 0.010 0.060 0.086 0.014 0.065 0.090 0.022 0.107 0.065 0.094 0.110
[13] 0.070 0.097 0.111 0.114
$IJ
I J Total
1 0.005583333 0.004416667 0.010
2 0.036916667 0.023083333 0.060
3 0.063583333 0.022416667 0.086
4 0.007916667 0.006083333 0.014
$I.perc
I
1 4.897661
2 32.383041
3 55.774854
4 6.944444
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