I read in one article published in top ranked journal where the authors ran null model before testing more complex model to calculate between- and within-group variance for job performance in their data set. I am trying to make sense of it but could not locate any helping material.
I will appreciate if someone can explain the purpose of the running null model in hierarchical linear modeling, its procedure and the interpretation of the output generated by null model.
Thank you.
One reason for doing this to get some sense of what needs to be explained. The null or empty model contains just one fixed term -the mean- and then a variance at each level, So in an educational context you would have the overall pupil score in the typical school and between school variation and within school between pupil variation. This will allow you to calculate the Intra class correlation which in this context gives the proportion of the total variation at the school level and also how similar pupils within a school are on the outcome. This variation is of course unexplained variation. You can then add variables in to fixed part at each level to see what happens to the unexplained variation. Adding in a pupil variable can reduce the school variance but could also increase it.
This classic early paper gives a very clear example of this variance decomposition
https://www.researchgate.net/publication/240473592_Statistical_Modelling_Issues_in_School_Effectiveness_Studies
And this site gives unrivalled resources
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html
Article Statistical Modelling Issues in School Effectiveness Studies
Before running more complex models, you need to know if there is significant variation at level 2. If there is no significant variation at level 2, you do not need to use HLM. If there is a variation, you then try to explain it by running full model. My attached article very simply shows using unconditional model and intra-class correlation. I hope it helps you to better understand the reason for running empty-unconditional model.
Article The effects of community factors on school participation in ...
Just to elaborate - I think is common advice, but is not necessarily always sensible. "Before running more complex models, you need to know if there is significant variation at level 2. If there is no significant variation at level 2, you do not need to use HLM."
Two counter-examples:
First, you may have complex structure that you want to account for in the design and you should not revert to a simpler model just because p > .05. One wouldn't do this with paired data just because the correlation between pairs was non-significant so why with multilevel data?
Second, if your primary research question is a complex one (e.g., a cross-level interaction or about random slopes) then regardless of the significance of love 2 variation in the null model you should fit the model that includes that effect.
Thank you all Kelvyn Jones, Sedat Gümüş and Thom S Baguley for your informative answers.
I would add to Thom' s comment - I have seen the unexplained variance at level 2 increase when a level 1 predictor is put in the model - it has previously been masked.
https://www.researchgate.net/profile/Kelvyn_Jones/publication/269902000_Amendment_to_'Specifying_and_Estimating_Multi-Level_Models_for_Geographical_Research'_by_Kelvyn_Jones_1991_Trans_Inst_Br_Geogr_16_148-160/links/55f459e208ae6a34f6608d30.pdf
Although of course the overall unexplained variance goes down.
Article Amendment to 'Specifying and Estimating Multi-Level Models f...
To legalize and justify the use of HLM, as to reach certainty that there is a discrepancy in the second level.
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