Totally agree with David Eugene Booth. This family of transformations is summarized in these three attached images. They will help you to choose, based on the lambda value, the appropriate transformation to make your data more homoscedastic and approximate its distribution to the normal distribution. Many softwares, including R of course, estimate the value of lambda and from there you induce the transformation to be performed or make the transformation directly.

Regards !

Mariel.

Hi I would try the Box-Cox family of transformations. Log belongs to that family but another member may work better for you. there is an automatic procedure in R- see this link:

https://www.google.com/search?q=Automated+box-cox+R&oq=Automated+box-cox+R&aqs=chrome..69i57.14507j0j8&sourceid=chrome&ie=UTF-8

Best wishes, David Booth

Totally agree with David Eugene Booth. This family of transformations is summarized in these three attached images. They will help you to choose, based on the lambda value, the appropriate transformation to make your data more homoscedastic and approximate its distribution to the normal distribution. Many softwares, including R of course, estimate the value of lambda and from there you induce the transformation to be performed or make the transformation directly.

Regards !

Mariel.

Dear all

I did not know about it: very useful! thanks!

However, I keep on having problems of heteroscedastisity despte t he new trasformation.

Do you have any other suggestion?

Thanks a lot in advance!

Best,

Martina

As well as a transformation , you can also explicitly model the heterogeneity in Y as a function of an X; see chapter 5

Book Developing multilevel models for analysing contextuality, he...

Thanks for the advice!

I have what I thought was a nice interesting use of what I think is Kelvyn's suggestion. The paper is attached. BTW plots are very helpful in this case. Best wishes, David Booth.

Hi, nice to meet you. thank you for responding, sorry for the long wait because of my survey busyness. For tests with Lisrel generally test the suitability of the model (Goodness of Fit Index) and the validity and reliability. Heteroscedasticity is usually tested if we use multiple regression as part of one of the classic assumption tests. In the lisrel test, do not use it. may be useful. thank you, greetings success always

I see no point in testing for it - you want to accommodate it , and you can do that through modelling.

Along the lines of what Kelvyn said, is there a missing explanatory variable that could explain the variance at larger pupil sizes? You can also run the box-cox transformations on your explanatory variables. Another option is to use robust estimation of mixed effects models which can reduce the influence of outliers. The package robustlmm in R can do this.