Walter Anderson
2011-Mar-29 13:57 UTC
[R] How to regress data into coefficients for a gamma function
Hello,
I need to regress data like the example below. The data points
represent friction factors derived from observed trip length data. The
function used to describe this data is a gamma function of the form,
f(t) = a * t^b * e^(c*t) and I need to regress the data to obtain the
a,b, and c coefficients. The gamma function can also be expressed in
the log-linear form, ln[f(t)] = ln[a] + b * ln[t] + c*t, which may be
easier to perform a regression on. I have performed a search for
information on the subject, and have found a few possibly related sites,
I can not figure out how to perform the regression in R. Any
help/guidance would be appreciated.
Walter
t f ln(f)
1 1 952893 13
2 2 951077 13
3 3 945991 13
4 4 942358 13
5 5 939452 13
6 6 895494 13
7 7 891861 13
8 8 882416 13
9 9 873697 13
10 10 867885 13
11 11 797771 13
12 12 791595 13
13 13 779243 13
14 14 773068 13
15 15 765802 13
16 16 635383 13
17 17 628481 13
18 18 620488 13
19 19 612859 13
20 20 609590 13
21 21 508597 13
22 22 503511 13
23 23 498425 13
24 24 490069 13
25 25 486073 13
26 26 422862 12
27 27 418866 12
28 28 415233 12
29 29 408331 12
30 30 405424 12
31 31 263380 12
32 32 261201 12
33 33 257204 12
34 34 252845 12
35 35 250665 12
36 36 209978 12
37 37 205981 12
38 38 203438 12
39 39 199079 12
40 40 197263 12
41 41 154758 11
42 42 152942 11
43 43 149309 11
44 44 148583 11
45 45 147493 11
46 46 98086 11
47 47 97723 11
48 48 95906 11
49 49 94090 11
50 50 93363 11
51 51 81738 11
52 52 81012 11
53 53 80649 11
54 54 79559 11
55 55 79195 11
56 56 70477 11
57 57 70477 11
58 58 70477 11
59 59 70477 11
60 60 70477 11
61 61 42867 10
62 62 42140 10
63 63 42140 10
64 64 42140 10
65 65 41777 10
66 66 36691 10
67 67 36328 10
68 68 35965 10
69 69 35965 10
70 70 35965 10
71 71 31968 10
72 72 31968 10
73 73 31968 10
74 74 31968 10
75 75 31605 10
76 76 21070 9
77 77 20707 9
78 78 20707 9
79 79 20343 9
80 80 19980 9
81 81 15984 9
82 82 15984 9
83 83 15984 9
84 84 15984 9
85 85 15984 9
86 86 14168 9
87 87 14168 9
88 88 14168 9
89 89 14168 9
90 90 14168 9
Peter Ehlers
2011-Mar-29 18:04 UTC
[R] How to regress data into coefficients for a gamma function
On 2011-03-29 06:57, Walter Anderson wrote:> Hello, > > I need to regress data like the example below. The data points > represent friction factors derived from observed trip length data. The > function used to describe this data is a gamma function of the form, > f(t) = a * t^b * e^(c*t) and I need to regress the data to obtain the > a,b, and c coefficients. The gamma function can also be expressed in > the log-linear form, ln[f(t)] = ln[a] + b * ln[t] + c*t, which may be > easier to perform a regression on. I have performed a search for > information on the subject, and have found a few possibly related sites, > I can not figure out how to perform the regression in R. Any > help/guidance would be appreciated. > > Walter > > t f ln(f) > 1 1 952893 13 > 2 2 951077 13 > 3 3 945991 13 > 4 4 942358 13 > 5 5 939452 13[... more data snipped ...] This looks like easy grist for the nls() mill. I would usually use the log form to get reasonable starting values for the nls interations: ## assume that your data are in a data.frame DF; fm1 <- lm( log(f) ~ log(t) + t, data = DF ) coef(fm1) # (Intercept) log(t) t # 13.81370501 0.18469223 -0.05955323 startvec <- c( aa=exp(14), bb=0.2, cc=-.06 ) fm2 <- nls( f ~ aa * t^bb * exp(cc*t), data=DF, start=startvec ) #summary(fm2) coef(fm2) # aa bb cc # 9.093841e+05 2.294895e-01 -5.951806e-02 ## plot the data plot( f ~ t, data=DF ) lines( fitted(fm2) ~ t, data=DF ) I wouldn't trust the model for small t. Peter Ehlers
JLucke at ria.buffalo.edu
2011-Mar-30 13:32 UTC
[R] How to regress data into coefficients for a gamma function
Regression for the gamma distribution can be expressed as a generalized
linear model. Check Chapter 8 of McCullagh, P. & Nelder, J. A. (1989),
Generalized linear models, Chapman & Hall, London, UK.
Walter Anderson <wandrson01@gmail.com>
Sent by: r-help-bounces@r-project.org
03/29/2011 09:57 AM
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Subject
[R] How to regress data into coefficients for a gamma function
Hello,
I need to regress data like the example below. The data points
represent friction factors derived from observed trip length data. The
function used to describe this data is a gamma function of the form,
f(t) = a * t^b * e^(c*t) and I need to regress the data to obtain the
a,b, and c coefficients. The gamma function can also be expressed in
the log-linear form, ln[f(t)] = ln[a] + b * ln[t] + c*t, which may be
easier to perform a regression on. I have performed a search for
information on the subject, and have found a few possibly related sites,
I can not figure out how to perform the regression in R. Any
help/guidance would be appreciated.
Walter
t f ln(f)
1 1 952893 13
2 2 951077 13
3 3 945991 13
4 4 942358 13
5 5 939452 13
6 6 895494 13
7 7 891861 13
8 8 882416 13
9 9 873697 13
10 10 867885 13
11 11 797771 13
12 12 791595 13
13 13 779243 13
14 14 773068 13
15 15 765802 13
16 16 635383 13
17 17 628481 13
18 18 620488 13
19 19 612859 13
20 20 609590 13
21 21 508597 13
22 22 503511 13
23 23 498425 13
24 24 490069 13
25 25 486073 13
26 26 422862 12
27 27 418866 12
28 28 415233 12
29 29 408331 12
30 30 405424 12
31 31 263380 12
32 32 261201 12
33 33 257204 12
34 34 252845 12
35 35 250665 12
36 36 209978 12
37 37 205981 12
38 38 203438 12
39 39 199079 12
40 40 197263 12
41 41 154758 11
42 42 152942 11
43 43 149309 11
44 44 148583 11
45 45 147493 11
46 46 98086 11
47 47 97723 11
48 48 95906 11
49 49 94090 11
50 50 93363 11
51 51 81738 11
52 52 81012 11
53 53 80649 11
54 54 79559 11
55 55 79195 11
56 56 70477 11
57 57 70477 11
58 58 70477 11
59 59 70477 11
60 60 70477 11
61 61 42867 10
62 62 42140 10
63 63 42140 10
64 64 42140 10
65 65 41777 10
66 66 36691 10
67 67 36328 10
68 68 35965 10
69 69 35965 10
70 70 35965 10
71 71 31968 10
72 72 31968 10
73 73 31968 10
74 74 31968 10
75 75 31605 10
76 76 21070 9
77 77 20707 9
78 78 20707 9
79 79 20343 9
80 80 19980 9
81 81 15984 9
82 82 15984 9
83 83 15984 9
84 84 15984 9
85 85 15984 9
86 86 14168 9
87 87 14168 9
88 88 14168 9
89 89 14168 9
90 90 14168 9
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