[R] Sum of Squares Type I, II, III for ANOVA
Thanh Tran
m@@ternh@ttt @ending from gm@il@com
Wed Nov 7 04:08:11 CET 2018
Dear Prof. John Fox,
Thank you for your advice. I will take care in the future post.
Best regards,
Nhat Tran
Vào Th 4, 7 thg 11, 2018 vào lúc 11:41 Fox, John <jfox using mcmaster.ca> đã
viết:
> Dear Thanh Tran,
>
> When you start a discussion on r-help, it's polite to keep it there so
> other people can see what transpires. I'm consequently cc'ing this response
> to the r-help list.
>
> The problem with your code is that anova(), as opposed to Anova(), has no
> type argument.
>
> Here's what I get with your data. I hope that the code and output don't
> get too mangled:
>
> > data <- read.csv("Saha research.csv", header=TRUE)
>
> > data <- within(data, {
> + tem <- as.factor(temperature)
> + ac <- as.factor (AC)
> + av <- as.factor(AV)
> + thick <- as.factor(Thickness)
> + })
>
> > library(car)
> Loading required package: carData
>
> > options(contrasts = c("contr.sum", "contr.poly"))
>
> > mod <- lm(KIC ~ tem*ac + tem*av + tem*thick + ac*av +ac*thick +
> av*thick,
> + data=data)
>
> > anova(mod) # type I (sequential)
> 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
>
> > Anova(mod) # type II
> Anova Table (Type II tests)
>
> Response: KIC
> Sum Sq Df F value Pr(>F)
> tem 15.3917 2 427.9926 < 2.2e-16 ***
> ac 0.1709 2 4.7510 0.0096967 **
> av 1.9097 1 106.2055 < 2.2e-16 ***
> thick 0.2041 2 5.6756 0.0040359 **
> tem:ac 0.5653 4 7.8598 6.973e-06 ***
> tem:av 1.7192 2 47.8046 < 2.2e-16 ***
> tem:thick 0.0728 4 1.0120 0.4024210
> ac:av 0.3175 2 8.8297 0.0002154 ***
> ac:thick 0.0883 4 1.2280 0.3003570
> av:thick 0.0662 2 1.8421 0.1613058
> Residuals 3.4164 190
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> > Anova(mod, type=3) # type III
> Anova Table (Type III tests)
>
> Response: KIC
> Sum Sq Df F value Pr(>F)
> (Intercept) 102.430 1 5696.4740 < 2.2e-16 ***
> tem 15.392 2 427.9926 < 2.2e-16 ***
> ac 0.171 2 4.7510 0.0096967 **
> av 1.910 1 106.2055 < 2.2e-16 ***
> thick 0.204 2 5.6756 0.0040359 **
> tem:ac 0.565 4 7.8598 6.973e-06 ***
> tem:av 1.719 2 47.8046 < 2.2e-16 ***
> tem:thick 0.073 4 1.0120 0.4024210
> ac:av 0.318 2 8.8297 0.0002154 ***
> ac:thick 0.088 4 1.2280 0.3003570
> av:thick 0.066 2 1.8421 0.1613058
> Residuals 3.416 190
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> If you have questions about Minitab there's probably another place to ask.
> It's not my opinion that type-III tests are generally preferable to type-II
> tests. Focus, in my opinion, should be on what hypotheses are being tested.
> If you want to see more detail, you could consult the book with which the
> car package is associated: see citation(package="car").
>
> Best,
> John
>
> > -----Original Message-----
> > From: Thanh Tran [mailto:masternhattt using gmail.com]
> > Sent: Tuesday, November 6, 2018 9:15 PM
> > To: Fox, John <jfox using mcmaster.ca>
> > Subject: Re: [R] Sum of Squares Type I, II, III for ANOVA
> >
> > Dear Prof. John Fox,
> > Thank you for your answer. The CSV data was added as the attached file
> again.
> > I try to set the contrasts properly *before* I fit the model but I
> received a
> > problem as follows.
> >
> > > setwd("C:/NHAT/HOC TAP/R/Test/Anova") 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)
> > > library(car)
> > Loading required package: carData
> > > options(contrasts = c("contr.sum", "contr.poly")) mod <- lm(KIC ~
> > > tem*ac + tem*av + tem*thick + ac*av +ac*thick + av*thick)
> > > anova(mod,type= 3)
> > Error: $ operator is invalid for atomic vectors
> >
> >
> > Another problem is that in the paper that I read, the authors used
> MINITAB to
> > analyze Anova. The authors use "adjusted sums of squares" calculate the
> p-
> > value. So which should I use? Type I adjusted SS or Type III sequential
> SS?
> > Minitab help tells me that I would "usually" want to use type III
> adjusted SS, as
> > type I sequential "sums of squares can differ when your design is
> unbalanced"
> > - which mine is. The R functions I am using are clearly using the type I
> > sequential SS.
> >
> > Thanks
> > Nhat Tran
> >
> >
> > Vào Th 4, 7 thg 11, 2018 vào lúc 10:41 Fox, John <jfox using mcmaster.ca
> > <mailto:jfox using mcmaster.ca> > đã viết:
> >
> >
> > 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-bounces using r-project.org <mailto:
> r-help-
> > bounces using r-project.org> ] On Behalf Of Thanh Tran
> > > Sent: Tuesday, November 6, 2018 6:58 PM
> > > To: r-help using r-project.org <mailto:r-help using 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 using r-project.org <mailto:R-help using r-project.org> mailing
> list --
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> > > and provide commented, minimal, self-contained, reproducible
> > code.
> >
>
>
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