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I have following two models (fit1, fit2) estimated using nls approach. I want to compare their goodness using anova, and the results follows: 

dd <- data.frame(t=0:10,
                 Frequency=c(195746,93938,53181,31853,19856,12182,
                             7847,5459,4325,3203,2750))
model1 <- deriv( ~ c*(1+b*(q-1)*t)^(1/(1-q)),
               c("c", "b", "q"), function (t, c, b,q){})

par1 <- list(c = 1e5, b = 1.5, q =2)
fit1 <- nls(Frequency ~ model1(t, c, b, q), data=dd,start=par1)

model3 <- deriv( ~  exp(-beta1*t)/(beta2+beta3*t),c("beta1", "beta2", "beta3"),
                function (t, beta1, beta2,beta3){})
par3 <- list(beta1 = .0100, beta2 = .0002, beta3 =0.0002)
fit3 <- nls(Frequency ~ model3(t, beta1,beta2,beta3), data=dd,start=par3)

anova(fit3,fit1,test="Chisq")


Model 1: Frequency ~ model(t, beta1, beta2, beta3)

Model 2: Frequency ~ model(t, c, b, q)
  Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
1     78   11892917                         
2     78   14080592  0      0

I am still not sure if I can use anova? Or if there is another approach I would appreciate it if you let me know about...

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    $\begingroup$ In what sense are these "nested"? They don't seem to have the same parameters. $\endgroup$
    – gung - Reinstate Monica
    Dec 20, 2016 at 19:08

1 Answer 1

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Chi-square test and the default F test are valid only if the the models are nested. Your models don't seem be nested, thus you can't interpret anything from it.

EDIT: Nested means the one of the model is a subset of the other model. Your model parameters suggest otherwise. None of your model is a subset of the other model. You can't apply anova() here. If you believe your models are nested, please give us a working script.

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  • $\begingroup$ fit1 and fit2 have different parameters, and they don't look like nested to me. Also pointed out by @gung. $\endgroup$
    – SmallChess
    Dec 21, 2016 at 0:06
  • $\begingroup$ @13554N I edited... $\endgroup$
    – SmallChess
    Dec 21, 2016 at 1:17
  • $\begingroup$ I edited my question and provided the working script.. $\endgroup$
    – 13554N
    Dec 21, 2016 at 17:01
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    $\begingroup$ @13554N I checked it, but I don't think they are nested. $\endgroup$
    – SmallChess
    Dec 23, 2016 at 1:08
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    $\begingroup$ @13554N If you want to compare the models, you might want to use AIC/BIC. They are okay for non-nested models. You may also want to use R2, adjusted R2. $\endgroup$
    – SmallChess
    Dec 23, 2016 at 1:09

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