Dear Nhat Tran, One more thing: You could specify the model even more compactly as
mod <- lm(KIC ~ (tem + ac + av + thick)^2) Best, John > -----Original Message----- > From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of Fox, John > Sent: Tuesday, November 6, 2018 8:41 PM > To: Thanh Tran <masternha...@gmail.com> > Cc: r-help@r-project.org > Subject: Re: [R] Sum of Squares Type I, II, III for ANOVA > > Dear Nhat Tran, > > The output that you show is unreadable and as far as I can see, the data > aren't > attached, but perhaps the following will help: First, if you want Anova() to > compute type III tests, then you have to set the contrasts properly *before* > you fit the model, not after. Second, you can specify the model much more > compactly as > > mod <- lm(KIC ~ tem*ac + tem*av + tem*thick + ac*av +ac*thick + av*thick) > > Finally, as sound general practice, I'd not attach the data, but rather put > your > recoded variables in the data frame and then specify the data argument to > lm(). > > I hope that this helps, > John > > ----------------------------------------------------------------- > John Fox > Professor Emeritus > McMaster University > Hamilton, Ontario, Canada > Web: https://socialsciences.mcmaster.ca/jfox/ > > > > > -----Original Message----- > > From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of Thanh > > Tran > > Sent: Tuesday, November 6, 2018 6:58 PM > > To: r-help@r-project.org > > Subject: [R] Sum of Squares Type I, II, III for ANOVA > > > > Hi everyone, > > I'm studying the ANOVA in R and have some questions to share. I > > investigate the effects of 4 factors (temperature-3 levels, asphalt > > content-3 levels, air > > voids-2 levels, and sample thickness-3 levels) on the hardness of > > asphalt concrete in the tensile test (abbreviated as KIC). These data > > were taken from a acticle paper. The codes were wrriten as the follows: > > > > > data = read.csv("Saha research.csv", header =T) > > > attach(data) > > > tem = as.factor(temperature) > > > ac= as.factor (AC) > > > av = as.factor(AV) > > > thick = as.factor(Thickness) > > > model = > > lm(KIC~tem+ac+av+thick+tem:ac+tem:av+tem:thick+ac:av+ac:thick+av:thick > > ) > > > anova(model) #Type I tests > > > library(car) Loading required package: carData > > > > anova(lm(KIC~tem+ac+av+thick+tem:ac+tem:av+tem:thick+ac:av+ac:thick+av > > :thick),type=2) > > Error: $ operator is invalid for atomic vectors > > > options(contrasts = c("contr.sum", "contr.poly")) > > > Anova(model,type="3") # Type III tests > > > Anova(model,type="2") # Type II tests > > > > With R, three results from Type I, II, and III almost have the same as > > follows. > > > > Analysis of Variance Table Response: KIC Df Sum Sq Mean Sq F value > > Pr(>F) tem 2 15.3917 7.6958 427.9926 < 2.2e-16 *** ac 2 0.1709 0.0854 > > 4.7510 > > 0.0096967 ** av 1 1.9097 1.9097 106.2055 < 2.2e-16 *** thick 2 0.2041 > > 0.1021 5.6756 0.0040359 ** tem:ac 4 0.5653 0.1413 7.8598 6.973e-06 *** > > tem:av 2 1.7192 0.8596 47.8046 < 2.2e-16 *** tem:thick 4 0.0728 0.0182 > > 1.0120 0.4024210 ac:av 2 0.3175 0.1588 8.8297 0.0002154 *** ac:thick 4 > > 0.0883 0.0221 1.2280 0.3003570 av:thick 2 0.0662 0.0331 1.8421 > > 0.1613058 Residuals 190 3.4164 0.0180 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ > 0.01 ‘*’ > > 0.05 ‘.’ 0.1 ‘ ’ 1 > > > > However, these results are different from the results in the article, > > especially for the interaction (air voids and sample thickness). The > > results presented in the article are as follows: > > Analysis of variance for KIC, using Adjusted SS for tests. Source DF > > Seq SS Adj MS F-stat P-value Model findings Temperature 2 15.39355 > > 7.69677 426.68 > > <0.01 Significant AC 2 0.95784 0.47892 26.55 <0.01 Significant AV 1 > > 0.57035 > > 0.57035 31.62 <0.01 Significant Thickness 2 0.20269 0.10135 5.62 <0.01 > > Significant Temperature⁄AC 4 1.37762 0.34441 19.09 <0.01 Significant > > Temperature⁄AV 2 0.8329 0.41645 23.09 <0.01 Significant > > Temperature⁄thickness 4 0.07135 0.01784 0.99 0.415 Not significant > > AC⁄AV 2 > > 0.86557 0.43279 23.99 <0.01 Significant AC⁄thickness 4 0.04337 0.01084 > > 0.6 > > 0.662 Not significant AV⁄thickness 2 0.17394 0.08697 4.82 <0.01 > > Significant Error 190 3.42734 0.01804 Total 215 23.91653 > > > > Therefore, I wonder that whether there is an error in my code or there > > is another type of ANOVA in R. If you could answer my problems, I > > would be most grateful. > > Best regards, > > Nhat Tran > > Ps: I also added a CSV file and the paper for practicing R. > > ______________________________________________ > > R-help@r-project.org 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. > ______________________________________________ > R-help@r-project.org 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. ______________________________________________ R-help@r-project.org 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.
