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  ASReml  ~  Which model better to use?

vsnshad1
Posted: Tue Sep 11, 2018 3:39 am Reply with quote
Joined: 06 Mar 2017 Posts: 16
Hi Everyone,

I am analyzing a dataset using asreml, in the first model with rcove=~ar1(Col):ar1(Row) (their effects are high and unconstrained) and no Row or Col effects or their linear effects, and in the second model only with lin(Row) and no rcov or random row and col parts.

lin(Row) is highly significant.

Loglikelihood for the first one is 167 and for the second one (with lin(Row)) is 76.

So I am wondering which model is better in this case?


Thank you for your help.

Best Regards
Mehrshad
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Arthur
Posted: Tue Sep 11, 2018 10:58 pm Reply with quote
Joined: 05 Aug 2008 Posts: 471 Location: Orange, NSW
Dear Mehrshad,

It is unclear to me what models you are comparing.

Four main possibilities are

yield ~ mu !r block variety # Basic RCB analysis
residual units

yield ~ mu lin(row) lin(col) !r row col block variety # Extended RCB analysis
residual units

yield ~ mu !r block variety # Basic spatial analysis
residual ar1(row).ar1(col)

yield ~ mu lin(row) lin(col) !r row col block variety # Extended spatial analysis
residual ar1(row).ar1(col)

and many intermediates.

Now comparing models 1 and 3, you can use a likelihood ratio test to test the significance
of the 2 residual spatial parameters. I gather they are significant.
Similarly, compare 2 with 4 this way.

You can test the significance of lin() terms in models 2 and 4 (Wald F statistic).
I gather lin(row) is significant in 2; and may also be in 4.

To find the best reduced model, it is a subjective process and depends somewhat on
the numbers of rows and columns, and the replication of genotypes, and the suitability of the randomization
for spatial analysis.

My experience is that often, spatial variation can be fitted as trends, as block/row/column effects and
as ARxAR spatial variation and it is not usually good to have all forms present in small experiments.
I am inclined to drop non-significant model terms and leave in the AR spatial variation.

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Arthur Gilmour

Retired Principal Research Scientist (Biometrics)
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vsnshad1
Posted: Wed Sep 12, 2018 1:26 am Reply with quote
Joined: 06 Mar 2017 Posts: 16
Hi Arthur,

Thanks for your comments and information.

Yes, I am using a spatial analysis as I have col*row design. First I start with a spatial part and then based on the Variogram I get an idea about the variation within the columns and rows and then check for the random and linear effects of the col and row. if the ar*ar is not significant I drop them from the model and check for the row and column in the random part.

As I mentioned in my previous post the linear Row was highly sig. but the loglik for the model with ar1*ar1, is nearly double compared to when I just have the linear Row as a covariate in the fixed part of the model.

I am using similar to modl4 in your post but the variety is considered as fixed.

Hope this makes a bit clear.

Regards
Mehrshad






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Arthur
Posted: Wed Sep 12, 2018 10:43 pm Reply with quote
Joined: 05 Aug 2008 Posts: 471 Location: Orange, NSW
Dear Mehrshad ,

I forgot to mention that LogL values ARE NOT COMPARABLE when the FIXED part of the model is changed.
Therefore, to test FIXED effects we use the Wald F statistic.

We use the LogL values to compare between models where only RANDOM terms have changed.
(The FIXED terms and their alliasing must not change).

A potential trap is when FIXED effects are included in the SPARSE equations. Changing the random model
may result in those fixed effects being fitted in a different order, potentially resulting in a change to the FIXED
model (if there is alliassing) and invalidating the REML comparison.

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Arthur Gilmour

Retired Principal Research Scientist (Biometrics)
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vsnshad1
Posted: Wed Sep 12, 2018 11:02 pm Reply with quote
Joined: 06 Mar 2017 Posts: 16
Dear Arthur,

Thanks for the comments.
What about AIC and BIC. I checked the AIC and BIC of the two models. got the same results.

Yes, I used wald test to see if the lin(row) or lin(col) are significant?


But the question is how should we decide when the linear effects of row or column are significant but AIC, BIC are lower for when we do not have linear row or column?


So you mean if we have SPARSE component we cannot compare two models with LL or AIC?

Regards

Mehrshad
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Arthur
Posted: Fri Oct 19, 2018 2:18 am Reply with quote
Joined: 05 Aug 2008 Posts: 471 Location: Orange, NSW
Dear Mehrshad,

Different people do different things so there is no obvious RIGHT approach.
You aim is to get a model that suits the data.

If there is strong autocorrelation, it can not always be modelled by row/coulmn effects/trends
because the latter assume independence of the other dimension.

My recommendation is to drop spatial correlation parameters last of all.

1) Use a Wald F statistic to test the lin(row)/lin(column) trends.
If not significant, any small effect will be picked up by the row/column random effect terms.

2) Use a likelihood ratio test (or AIC/BIC) to test the row/column random effects.
If not significant, drop them because the spatial ar parameters will soak up any small effect
that remains.

3) I am generally happy to leave the spatial AR parameters in the model
even if they are not significant, unless you are vary short of degrees of freedom.

The spatial AR parameters can accommodate patterns in the residuals that are
not able to be modelled by lin(row)/lin(column) or row/column.

_________________
Arthur Gilmour

Retired Principal Research Scientist (Biometrics)
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