# Test individual slope for each factor level in ANCOVA

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## Test individual slope for each factor level in ANCOVA

 Hi all,    Consider the data set where there are a continuous response variable, a continuous predictor "weeks" and a categorical variable "region" with five levels "a", "b", "c", "d", "e".   I fit the ANCOVA model as follows. Here the reference level is region "a" and there are 4 dummy variables. The interaction terms (in red below) represent the slope difference between each region and  the baseline region "a" and the corresponding p-value is for testing whether this slope difference is zero. Is there a way to directly test whether the slope corresponding to each individual factor level is 0 or not, instead of testing the slope difference from the baseline level?   Thanks very much.       Hanna > mod <- lm(response ~ weeks*region,data)> summary(mod) Call: lm(formula = response ~ weeks * region, data = data) Residuals:      Min       1Q   Median       3Q      Max -0.19228 -0.07433 -0.01283  0.04439  0.24544 Coefficients:                 Estimate Std. Error t value Pr(>|t|) (Intercept)    1.2105556  0.0954567  12.682  1.2e-14 *** weeks         -0.0213333  0.0147293  -1.448    0.156 regionb       -0.0257778  0.1349962  -0.191    0.850 regionc       -0.0344444  0.1349962  -0.255    0.800 regiond       -0.0754444  0.1349962  -0.559    0.580 regione       -0.1482222  0.1349962  -1.098    0.280    weeks:regionb -0.0007222  0.0208304  -0.035    0.973 weeks:regionc -0.0017778  0.0208304  -0.085    0.932 weeks:regiond  0.0030000  0.0208304   0.144    0.886 weeks:regione  0.0301667  0.0208304   1.448    0.156    --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.1082 on 35 degrees of freedom Multiple R-squared:  0.2678, Adjusted R-squared:  0.07946 F-statistic: 1.422 on 9 and 35 DF,  p-value: 0.2165         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Test individual slope for each factor level in ANCOVA

 Dear Hanna, You can test the slope in each non-reference group as a linear hypothesis. You didn’t make the data available for your example, so here’s an example using the linearHypothesis() function in the car package with the Moore data set in the same package: - - - snip - - - > library(car) > mod <- lm(conformity ~ fscore*partner.status, data=Moore) > summary(mod) Call: lm(formula = conformity ~ fscore * partner.status, data = Moore) Residuals:     Min      1Q  Median      3Q     Max -7.5296 -2.5984 -0.4473  2.0994 12.4704 Coefficients:                           Estimate Std. Error t value Pr(>|t|) (Intercept)               20.79348    3.26273   6.373 1.27e-07 *** fscore                    -0.15110    0.07171  -2.107  0.04127 * partner.statuslow        -15.53408    4.40045  -3.530  0.00104 ** fscore:partner.statuslow   0.26110    0.09700   2.692  0.01024 * --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 4.562 on 41 degrees of freedom Multiple R-squared:  0.2942, Adjusted R-squared:  0.2426 F-statistic: 5.698 on 3 and 41 DF,  p-value: 0.002347 > linearHypothesis(mod, "fscore + fscore:partner.statuslow") Linear hypothesis test Hypothesis: fscore  + fscore:partner.statuslow = 0 Model 1: restricted model Model 2: conformity ~ fscore * partner.status   Res.Df    RSS Df Sum of Sq      F  Pr(>F) 1     42 912.45     2     41 853.42  1    59.037 2.8363 0.09976 . --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 - - - snip - - - In this case, there are just two levels for partner.status, but for a multi-level factor you can simply perform more than one test. I hope this helps,  John ------------------------------------- John Fox, Professor McMaster University Hamilton, Ontario, Canada Web: http://socserv.mcmaster.ca/jfox/On 2017-03-15, 9:43 PM, "R-help on behalf of li li" <[hidden email] on behalf of [hidden email]> wrote: >Hi all, >   Consider the data set where there are a continuous response variable, a >continuous predictor "weeks" and a categorical variable "region" with five >levels "a", "b", "c", >"d", "e". >  I fit the ANCOVA model as follows. Here the reference level is region >"a" >and there are 4 dummy variables. The interaction terms (in red below) >represent the slope >difference between each region and  the baseline region "a" and the >corresponding p-value is for testing whether this slope difference is >zero. >Is there a way to directly test whether the slope corresponding to each >individual factor level is 0 or not, instead of testing the slope >difference from the baseline level? >  Thanks very much. >      Hanna > > > > > > >> mod <- lm(response ~ weeks*region,data)> summary(mod) >Call: >lm(formula = response ~ weeks * region, data = data) > >Residuals: >     Min       1Q   Median       3Q      Max >-0.19228 -0.07433 -0.01283  0.04439  0.24544 > >Coefficients: >                Estimate Std. Error t value Pr(>|t|) >(Intercept)    1.2105556  0.0954567  12.682  1.2e-14 *** >weeks         -0.0213333  0.0147293  -1.448    0.156 >regionb       -0.0257778  0.1349962  -0.191    0.850 >regionc       -0.0344444  0.1349962  -0.255    0.800 >regiond       -0.0754444  0.1349962  -0.559    0.580 >regione       -0.1482222  0.1349962  -1.098    0.280    weeks:regionb >-0.0007222  0.0208304  -0.035    0.973 >weeks:regionc -0.0017778  0.0208304  -0.085    0.932 >weeks:regiond  0.0030000  0.0208304   0.144    0.886 >weeks:regione  0.0301667  0.0208304   1.448    0.156    --- >Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > >Residual standard error: 0.1082 on 35 degrees of freedom >Multiple R-squared:  0.2678, Adjusted R-squared:  0.07946 >F-statistic: 1.422 on 9 and 35 DF,  p-value: 0.2165 > > [[alternative HTML version deleted]] > >______________________________________________ >[hidden email] mailing list -- To UNSUBSCRIBE and more, see >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. ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.