The study randomized participants by Source (Expert vs Attractive) and by Argument (Strong vs Weak), were categorized into Monitor type (High vs Low). I want to test the significance of the main effects, the two-way interactions, and the three-way interactions of the following dataframe - specifically,
Main effects = Self-Monitors (High vs. Low), Argument (Strong vs. Weak), Source (Attractive vs. Expert)
Two-way interactions = Self-MonitorsArgument, Self-MonitorsSource, Argument*Source
Three-way interactions = Self-MonitorsArgumentSource
This is the code:
data<-data.frame(Monitor=c(rep("High.Self.Monitors", 24),rep("Low.Self.Monitors", 24)),
Argument=c(rep("Strong", 24), rep("Weak", 24), rep("Strong", 24), rep("Weak", 24)),
Source=c(rep("Expert",12),rep("Attractive",12),rep("Expert",12),rep("Attractive",12),
rep("Expert",12),rep("Attractive",12),rep("Expert",12),rep("Attractive",12)),
Response=c(4,3,4,5,2,5,4,6,3,4,5,4,4,4,2,3,5,3,2,3,4,3,2,4,3,5,3,2,6,4,4,3,5,3,2,3,5,5,7,5,6,4,3,5,6,7,7,6,
3,5,5,4,3,2,1,5,3,4,3,4,5,4,3,2,4,6,2,4,4,3,4,3,5,6,4,7,6,7,5,6,4,6,7,5,6,4,4,2,4,5,4,3,4,2,3,4))
data$Monitor<-as.factor(data$Monitor)
data$Argument<-as.factor(data$Argument)
data$Source<-as.factor(data$Source)
I'd like to obtain the main effects, as well as all two-way interactions and the three-way interaction. However, if I type in anova(lm(Response ~ Monitor*Argument*Source, data=data)) I obtain:
Analysis of Variance Table
Response: Response
Df Sum Sq Mean Sq F value Pr(>F)
Monitor 1 24.000 24.0000 13.5322 0.0003947 ***
Source 1 0.667 0.6667 0.3759 0.5413218
Monitor:Source 1 0.667 0.6667 0.3759 0.5413218
Residuals 92 163.167 1.7736
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
and if I enter summary(aov(Response ~ Monitor*Argument*Source, data=data))
Call:
lm.default(formula = Response ~ Monitor * Argument * Source,
data = data)
Residuals:
Min 1Q Median 3Q Max
-2.7917 -0.7917 0.2083 1.2083 2.5417
Coefficients: (4 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.4583 0.2718 12.722 < 2e-16 ***
MonitorLow.Self.Monitors 1.1667 0.3844 3.035 0.00313 **
ArgumentWeak NA NA NA NA
SourceExpert 0.3333 0.3844 0.867 0.38817
MonitorLow.Self.Monitors:ArgumentWeak NA NA NA NA
MonitorLow.Self.Monitors:SourceExpert -0.3333 0.5437 -0.613 0.54132
ArgumentWeak:SourceExpert NA NA NA NA
MonitorLow.Self.Monitors:ArgumentWeak:SourceExpert NA NA NA NA
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.332 on 92 degrees of freedom
Multiple R-squared: 0.1344, Adjusted R-squared: 0.1062
F-statistic: 4.761 on 3 and 92 DF, p-value: 0.00394
Any thoughts or ideas?
Edit
Your data isn't well randomized as you say. In order to estimate a three-way interaction you'd have to have a group of subjects having "Low", "Strong" and "Expert" combination of levels of the three factors. You do not have such a group.
Look at:
table(data[,1:3])
For example.
In the example data set found below I want to calculate the proportion of variance in science explained by each independent variable using linear regression model. How could I achieve that in R?
hsb2 <- read.table('http://www.ats.ucla.edu/stat/r/modules/hsb2.csv', header=T, sep=",")
m1<-lm(science ~ math+female+ socst+ read, data =hsb2)
One of the ways is to use anova() function from stats package.
It gives you the residual sum of squares explained by each variable and total sum of squares (i.e. variance)
anova(m1)
Analysis of Variance Table
Response: science
Df Sum Sq Mean Sq F value Pr(>F)
math 1 7760.6 7760.6 151.8810 < 2.2e-16 ***
female 1 233.0 233.0 4.5599 0.033977 *
socst 1 465.6 465.6 9.1128 0.002878 **
read 1 1084.5 1084.5 21.2254 7.363e-06 ***
Residuals 195 9963.8 51.1
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
I am running a regression on R
fbReg <- lm(y~x2+x7+x8,table.b1)
I then run an Anova table to analyze the significance of the regression
anova(fbReg)
Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
x2 1 76.193 76.193 26.172 3.100e-05 ***
x7 1 139.501 139.501 47.918 3.698e-07 ***
x8 1 41.400 41.400 14.221 0.0009378 ***
Residuals 24 69.870 2.911
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Is there anything i can do to make my anova table sum all the sum of squares for x2,x7,x8 instead of having them separate.
Essentially, have the anova table look like this
df SS MS FvAL PR(>F)
Regression 3 257.094 ETC....
Error(Residual) 24 69.870 ETC.....
Thanks
To illustrate my comment:
> lm2 <- lm(Fertility ~ Catholic+Education+Agriculture, data = swiss)
> lm1 <- lm(Fertility ~ 1, data = swiss)
> anova(lm1,lm2)
Analysis of Variance Table
Model 1: Fertility ~ 1
Model 2: Fertility ~ Catholic + Education + Agriculture
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 7178.0
2 43 2567.9 3 4610.1 25.732 1.089e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
I am trying to analyze some visual transect data of organisms to generate a habitat distribution model. Once organisms are sighted, they are followed as point data is collected at a given time interval. Because of the autocorrelation among these "follows," I wish to utilize a GAM-GEE approach similar to that of Pirotta et al. 2011, using packages 'yags' and 'splines' (http://www.int-res.com/abstracts/meps/v436/p257-272/). Their R scripts are shown here (http://www.int-res.com/articles/suppl/m436p257_supp/m436p257_supp1-code.r). I have used this code with limited success and multiple issues of models failing to converge.
Below is the structure of my data:
> str(dat2)
'data.frame': 10792 obs. of 4 variables:
$ dist_slag : num 26475 26340 25886 25400 24934 ...
$ Depth : num -10.1 -10.5 -16.6 -22.2 -29.7 ...
$ dolphin_presence: int 0 0 0 0 0 0 0 0 0 0 ...
$ block : int 1 1 1 1 1 1 1 1 1 1 ...
> head(dat2)
dist_slag Depth dolphin_presence block
1 26475.47 -10.0934 0 1
2 26340.47 -10.4870 0 1
3 25886.33 -16.5752 0 1
4 25399.88 -22.2474 0 1
5 24934.29 -29.6797 0 1
6 24519.90 -26.2370 0 1
Here is the summary of my block variable (indicating the number of groups for which autocorrelation exists within each block
> summary(dat2$block)
Min. 1st Qu. Median Mean 3rd Qu. Max.
1.00 39.00 76.00 73.52 111.00 148.00
However, I would like to use the package 'gamm4', as I am more familiar with Professor Simon Wood's packages and functions, and it appears gamm4 might be the most appropriate. It is important to note that the models have a binary response (organism presence of absence along a transect), and thus why I think gamm4 is more appropriate than gamm. In the gamm help, it provides the following example for autocorrelation within factors:
## more complicated autocorrelation example - AR errors
## only within groups defined by `fac'
e <- rnorm(n,0,sig)
for (i in 2:n) e[i] <- 0.6*e[i-1]*(fac[i-1]==fac[i]) + e[i]
y <- f + e
b <- gamm(y~s(x,k=20),correlation=corAR1(form=~1|fac))
Following this example, the following is the code I used for my dataset
b <- gamm4(dolphin_presence~s(dist_slag)+s(Depth),random=(form=~1|block), family=binomial(),data=dat)
However, by examining the output (summary(b$gam)) and specifically summary(b$mer)), I am either unsure of how to interpret the results, or do not believe that the autocorrelation within the group is being taken into consideration.
> summary(b$gam)
Family: binomial
Link function: logit
Formula:
dolphin_presence ~ s(dist_slag) + s(Depth)
Parametric coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -13.968 5.145 -2.715 0.00663 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Approximate significance of smooth terms:
edf Ref.df Chi.sq p-value
s(dist_slag) 4.943 4.943 70.67 6.85e-14 ***
s(Depth) 6.869 6.869 115.59 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
R-sq.(adj) = 0.317glmer.ML score = 10504 Scale est. = 1 n = 10792
>
> summary(b$mer)
Generalized linear mixed model fit by the Laplace approximation
AIC BIC logLik deviance
10514 10551 -5252 10504
Random effects:
Groups Name Variance Std.Dev.
Xr s(dist_slag) 1611344 1269.39
Xr.0 s(Depth) 98622 314.04
Number of obs: 10792, groups: Xr, 8; Xr.0, 8
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
X(Intercept) -13.968 5.145 -2.715 0.00663 **
Xs(dist_slag)Fx1 -35.871 33.944 -1.057 0.29063
Xs(Depth)Fx1 3.971 3.740 1.062 0.28823
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
X(Int) X(_)F1
Xs(dst_s)F1 0.654
Xs(Dpth)Fx1 -0.030 0.000
>
How do I ensure that autocorrelation is indeed being accounted for within each unique value of the "block" variable? What is the simplest way to interpret the output for "summary(b$mer)"?
The results do differ from a normal gam (package mgcv) using the same variables and parameters without the "correlation=..." term, indicating that something different is occurring.
However, when I use a different variable for the correlation term (season), I get the SAME output:
> dat2 <- data.frame(dist_slag = dat$dist_slag, Depth = dat$Depth, dolphin_presence = dat$dolphin_presence,
+ block = dat$block, season=dat$season)
> head(dat2)
dist_slag Depth dolphin_presence block season
1 26475.47 -10.0934 0 1 F
2 26340.47 -10.4870 0 1 F
3 25886.33 -16.5752 0 1 F
4 25399.88 -22.2474 0 1 F
5 24934.29 -29.6797 0 1 F
6 24519.90 -26.2370 0 1 F
> summary(dat2$season)
F S
3224 7568
> b <- gamm4(dolphin_presence~s(dist_slag)+s(Depth),correlation=corAR1(1, form=~1 | season), family=binomial(),data=dat2)
> summary(b$gam)
Family: binomial
Link function: logit
Formula:
dolphin_presence ~ s(dist_slag) + s(Depth)
Parametric coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -13.968 5.145 -2.715 0.00663 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Approximate significance of smooth terms:
edf Ref.df Chi.sq p-value
s(dist_slag) 4.943 4.943 70.67 6.85e-14 ***
s(Depth) 6.869 6.869 115.59 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
R-sq.(adj) = 0.317glmer.ML score = 10504 Scale est. = 1 n = 10792
> summary(b$mer)
Generalized linear mixed model fit by the Laplace approximation
AIC BIC logLik deviance
10514 10551 -5252 10504
Random effects:
Groups Name Variance Std.Dev.
Xr s(dist_slag) 1611344 1269.39
Xr.0 s(Depth) 98622 314.04
Number of obs: 10792, groups: Xr, 8; Xr.0, 8
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
X(Intercept) -13.968 5.145 -2.715 0.00663 **
Xs(dist_slag)Fx1 -35.871 33.944 -1.057 0.29063
Xs(Depth)Fx1 3.971 3.740 1.062 0.28823
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
X(Int) X(_)F1
Xs(dst_s)F1 0.654
Xs(Dpth)Fx1 -0.030 0.000
>
I just want to make sure it is correctly allowing for correlation within each value for the "block" variable. How do I formulate the model to say that autocorrelation can exist within each single value for block, but assume independence among blocks?
On another note, I am also receiving the following warning message after model completion for larger models (with many more variables than 2):
Warning message:
In mer_finalize(ans) : false convergence (8)
gamm4 is built on top of lme4, which does not allow for a correlation parameter (in contrast to the nlme, package, which underlies mgcv::gamm). mgcv::gamm does handle binary data, although it uses PQL, which is generally less accurate than Laplace/GHQ approximations as in gamm4/lme4. It is unfortunate (!!) that you're not getting a warning telling you that the correlation argument is being ignored (when I try a simple example using a correlation argument with lme4, I do get a warning, but it's possible that the extra argument is getting swallowed somewhere inside gamm4).
Your desired autocorrelation structure ("autocorrelation can exist within each single value for block, but assume independence among blocks") is exactly the way correlation structures are coded in nlme (and hence in mgcv::gamm).
I would use mcgv::gamm, and would suggest that if at all possible you try it out on some simulated data with known structure (or use the data set provided in the supplementary material above and see if you can reproduce their qualitative conclusions with your alternative approach).
StackOverflow is nice, but there is probably more mixed model expertise at r-sig-mixed-models#r-project.org
The following script
#!/usr/bin/Rscript --vanilla
x <- c(4.5,6.4,7.2,6.7,8.8,7.8,9.6,7.0,5.9,6.8,5.7,5.2)
fertilizer<- factor(c('A','A','A','A','B','B','B','B','C','C','C','C'))
crop <- factor(c('I','II','III','IV','I','II','III','IV','I','II','III','IV'))
av <- aov(x~fertilizer*crop)
summary(av)
yields
Df Sum Sq Mean Sq
fertilizer 2 13.6800 6.8400
crop 3 2.8200 0.9400
fertilizer:crop 6 6.5800 1.0967
For other data, aov usually gives the F-statistic and associated p-value. What is wrong/special about this data that causes R to omit the juicy parts?
Should you using + instead of * in the formula?
> summary(aov(x~fertilizer + crop))
Df Sum Sq Mean Sq F value Pr(>F)
fertilizer 2 13.6800 6.8400 6.2371 0.03426 *
crop 3 2.8200 0.9400 0.8571 0.51218
Residuals 6 6.5800 1.0967
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1