Hallman, Tyler
2013-Apr-23 18:02 UTC
[R] Writing contrast statements to test difference of slope in linear regressions
Hi Everyone,
I am uncertain that I am writing the contrast statements correctly. Basically,
I'm unsure when to use a -1 and a 1 when writing the contrasts. Specifically
I am interested in comparing the slopes between different temperature regimes.
Temperature is therefore a factor. Time and percent are numerical. Using the
gmodels package I made the following model:
m2<-lm(Percent~Time+Temperature, data=Hchrys.Temp);summary(m2)
# results from m2
Call:
lm(formula = Percent ~ Time + Temperature, data = Hchrys.Temp)
Residuals:
Min 1Q Median 3Q Max
-0.098333 -0.031667 -0.003333 0.026667 0.101667
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.0233333 0.0147504 -1.582 0.119413
Time 0.0007639 0.0001774 4.306 6.91e-05 ***
Temperature22:18 0.0133333 0.0170324 0.783 0.437088
Temperature22:20 0.0133333 0.0170324 0.783 0.437088
Temperature22:22 0.0666667 0.0170324 3.914 0.000252 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.04665 on 55 degrees of freedom
Multiple R-squared: 0.3997, Adjusted R-squared: 0.356
F-statistic: 9.154 on 4 and 55 DF, p-value: 9.653e-06
# I then built the contrasts based on the order of the coefficients above.
cm1<-rbind("1:Temperature 20:20 v.22:22 " = c(0,0,0,0,1),
"2:Temperature 22:18 v.22:22 " = c(0,0,-1,0,1),
"3:Temperature 22:20 v.22:22 " = c(0,0,0,-1,1),
"4:Temperature 20:20 v.22:20 " = c(0,0,0,1,0),
"5:Temperature 22:18 v.22:20 " = c(0,0,-1,1,0),
"6:Temperature 20:20 v.22:18 " = c(0,0,1,0,0))
# To compare between them I used:
estimable(m2,cm1)
# The results of which are below.
Estimate Std. Error t value DF
Pr(>|t|)
1:Temperature 20:20 v.22:22 6.666667e-02 0.01703235 3.914120e+00 55
0.0002522632
2:Temperature 22:18 v.22:22 5.333333e-02 0.01703235 3.131296e+00 55
0.0027865530
3:Temperature 22:20 v.22:22 5.333333e-02 0.01703235 3.131296e+00 55
0.0027865530
4:Temperature 20:20 v.22:20 1.333333e-02 0.01703235 7.828240e-01 55
0.4370882317
5:Temperature 22:18 v.22:20 -3.469447e-17 0.01703235 -2.036975e-15 55
1.0000000000
6:Temperature 20:20 v.22:18 1.333333e-02 0.01703235 7.828240e-01 55
0.4370882317
Did I write the contrasts correctly? And does this then indicate that the slope
of 22:22 was significantly different from all others but none of the others were
different?
Help with comparing the slopes between these regressions would be wonderful.
Cheers,
-
Tyler Hallman, M.S.
Ph.D. Student
The Robinson Lab
Department of Fisheries and Wildlife
Oregon State University Corvallis
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Cade, Brian
2013-Apr-23 18:51 UTC
[R] Writing contrast statements to test difference of slope in linear regressions
Tyler: To compare estimates of different slopes for Time by different factor levels of Temperature you need to estimate a model that allows for separate slopes. What you've estimated is a model for just different intercepts associated with Temperature factor but a common slope for Time. You probably want a model that allows for both separate intercepts and slopes for Time across the Temperature factor levels. Try lm(Percent ~ Time + Temperature + Time:Temperature); the Temperature effects will describe differences in intercepts by factor levels and the Time:Temperature interactions are differences in slopes (Time) across factor levels. Brian Brian S. Cade, PhD U. S. Geological Survey Fort Collins Science Center 2150 Centre Ave., Bldg. C Fort Collins, CO 80526-8818 email: cadeb@usgs.gov <brian_cade@usgs.gov> tel: 970 226-9326 On Tue, Apr 23, 2013 at 12:02 PM, Hallman, Tyler < Tyler.Hallman@oregonstate.edu> wrote:> Hi Everyone, > > I am uncertain that I am writing the contrast statements correctly. > Basically, I'm unsure when to use a -1 and a 1 when writing the contrasts. > Specifically I am interested in comparing the slopes between different > temperature regimes. Temperature is therefore a factor. Time and percent > are numerical. Using the gmodels package I made the following model: > > m2<-lm(Percent~Time+Temperature, data=Hchrys.Temp);summary(m2) > > # results from m2 > Call: > lm(formula = Percent ~ Time + Temperature, data = Hchrys.Temp) > > Residuals: > Min 1Q Median 3Q Max > -0.098333 -0.031667 -0.003333 0.026667 0.101667 > > Coefficients: > Estimate Std. Error t value Pr(>|t|) > (Intercept) -0.0233333 0.0147504 -1.582 0.119413 > Time 0.0007639 0.0001774 4.306 6.91e-05 *** > Temperature22:18 0.0133333 0.0170324 0.783 0.437088 > Temperature22:20 0.0133333 0.0170324 0.783 0.437088 > Temperature22:22 0.0666667 0.0170324 3.914 0.000252 *** > --- > Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > Residual standard error: 0.04665 on 55 degrees of freedom > Multiple R-squared: 0.3997, Adjusted R-squared: 0.356 > F-statistic: 9.154 on 4 and 55 DF, p-value: 9.653e-06 > > # I then built the contrasts based on the order of the coefficients above. > > cm1<-rbind("1:Temperature 20:20 v.22:22 " = c(0,0,0,0,1), > "2:Temperature 22:18 v.22:22 " = c(0,0,-1,0,1), > "3:Temperature 22:20 v.22:22 " = c(0,0,0,-1,1), > "4:Temperature 20:20 v.22:20 " = c(0,0,0,1,0), > "5:Temperature 22:18 v.22:20 " = c(0,0,-1,1,0), > "6:Temperature 20:20 v.22:18 " = c(0,0,1,0,0)) > > # To compare between them I used: > estimable(m2,cm1) > > # The results of which are below. > Estimate Std. Error t value DF > Pr(>|t|) > 1:Temperature 20:20 v.22:22 6.666667e-02 0.01703235 3.914120e+00 55 > 0.0002522632 > 2:Temperature 22:18 v.22:22 5.333333e-02 0.01703235 3.131296e+00 55 > 0.0027865530 > 3:Temperature 22:20 v.22:22 5.333333e-02 0.01703235 3.131296e+00 55 > 0.0027865530 > 4:Temperature 20:20 v.22:20 1.333333e-02 0.01703235 7.828240e-01 55 > 0.4370882317 > 5:Temperature 22:18 v.22:20 -3.469447e-17 0.01703235 -2.036975e-15 55 > 1.0000000000 > 6:Temperature 20:20 v.22:18 1.333333e-02 0.01703235 7.828240e-01 55 > 0.4370882317 > > Did I write the contrasts correctly? And does this then indicate that the > slope of 22:22 was significantly different from all others but none of the > others were different? > > Help with comparing the slopes between these regressions would be > wonderful. > > Cheers, > > - > Tyler Hallman, M.S. > Ph.D. Student > The Robinson Lab > Department of Fisheries and Wildlife > Oregon State University Corvallis > > [[alternative HTML version deleted]] > > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > >[[alternative HTML version deleted]]