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I am comparing NLS models from two groups, males and females. I compared the models by ANOVAs, but I am hesitating which is the correct model comparison to use:

a) Subgroup Males vs Subgroup Females

b) All data (males and females) vs Subgroup Males (the smaller group in terms of sample size)

Bates and Pinheiro mentioned in their book, in chapter 8, to use the smaller group vs the whole sample. But, their example involved more than 2 groups.

I received the suggestion to add my code, so here it is:

I am using the von Bertalanffy growth function and the nlstools package from R:
function (t, Linf, K = NULL, L0 = NULL) 
{
    if (length(Linf) == 3) {
        K <- Linf[[2]]
        L0 <- Linf[[3]]
        Linf <- Linf[[1]]
    }
    Linf - (Linf - L0) * exp(-K * t)
}

Based on the Kumura (2015) paper and equations: LIKELIHOOD METHODS FOR THE VON BERTALANFFY GROWTH CURVE

Subsetting the data "df" into:

Males_df and Females_df

Stating the initial parameters with the vbsStarts Function in R:

svTLength_All <- vbStarts(Length~Age,data=df,type="vonBertalanffy")

svTFemales_Length<- vbStarts(Length~Age,data=Females_df,type="vonBertalanffy")


svTMales_Length<- vbStarts(Length~Age,data=Males_df,type="vonBertalanffy")

Fitting the models with those values:

fitLength_All <- nls(Length~vbT(Age,Linf,K,L0),data=df,start=svTLength_All)

fitLength_Females <- nls(Length~vbT(Age,Linf,K,L0),data=Females_df,start=svTFemales_Length)


fitLength_Males <- nls(Length~vbT(Age,Linf,K,L0),data=Males_df,start=svTMales_Length)

The sample sizes are n=42 for Females and n=35 for males.

The plot looks like this (x axis = Age in months):

Growthcurves based on von Bertalanffy models

I want to know if the difference between the growth curves from males and females is statistically significant.

I understand that an ANOVA between NLS models should include a hierarchical relation and Bates and Pinheiro mention, in chapter 6 from their book, that the best is to compare the model including the full data (fitLength_All, in this case) to the model estimated from the smaller group (fitLength_Males, in this case).

So I compared:

anova(fitLength_All, fitLength_Males)

I am still not sure that this is the best way to compare males vs females. For me taht anova would mean if males are the overall population are te same. When I do teh same for females:

anova(fitLength_All, fitLength_Females)

or between males and females:

anova(fitLength_Males, fitLength_Females)

The results vary greatly. I am not fully comfortable reporting differences only if the anova was significant between "All" (df) and the subgroup males [anova(fitLength_All, fitLength_Males)]. I am looking for advice on how to compare those growth curves statistically or for reassurance in case that anova is the correct way. If so, how may I interpret it?

User1865345
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Cris
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  • What exactly does "I am comparing NLS models from two groups, males and females." mean? – Roland May 02 '19 at 06:18
  • Thanks and sorry for not being clear enough. I mean that from a full data set, I am comparing two nls models based on the sub-groups males and females. Comparing by ANOVA if the models are the same for both sub-groups. There are models from growth curves, so for each 2 the models the variables (asymptote, growth rate and inflection) are specified independently. – Cris May 03 '19 at 19:30
  • @Roland , I'm learning to comment in this blog. I just found out I should have tagged you. Thanks for your response again. – Cris May 04 '19 at 14:48
  • You should show your code. Maybe this is helpful: https://stats.stackexchange.com/a/345703/11849 Also, package nlme offers facilities for nonlinear models coupled with linear models for the parameters: https://stat.ethz.ch/R-manual/R-devel/library/nlme/html/gnls.html – Roland May 04 '19 at 17:26
  • @Roland Ok, I added my code, hope it helps to clarify. I cannot use NLME since I do not have random effects on my models. – Cris May 04 '19 at 19:04
  • gnls does not include random effects. You should create two gnls models (one with parameters ~ group and one with parameters ~ 1) and compare these. – Roland May 04 '19 at 20:41

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