[R] Modelling heteroskedasticity in a multilevel model

[Spencer Graves]

	  I generally prefer to start with the distributional characteristics 
of the data, then consider "fixed effets" / explanatory variables, then 
dependence structure in the deviations from the model.

	  1.  What is (are) your response variable(s)?  If the numbers are 
financial numbers of volume of sales in whatever units and can never be 
negative, I would automatically take logarithms before I did anything 
else -- possibly after replacing any 0's by some small positive number 
to prevent sending part of the data to (-Inf).  Have you made normal 
probability plots and time series plots by company?  If it's something 
like stock prices, I might focus on first differences of something like 
log(price per share).  (And where are you getting your data?  For 
certain financial research questions, you need include dividends 
appropriately when computing "total increase in shareholder value".  I 
believe the Center for Research in Securities P rices at the University 
of Chicago does a fairly good job of this, and it's probably difficult 
to match what they do.)

	  2.  If you've appropriately transformed your data, what have you done 
to explore the relationships between your response variables and 
potential explanatory variables?  Plots, preceeded or followed by "lm" 
fits are wise.

	  3.  Then I want to consider residuals, by industry and correlated 
over time -- and correlations in absolute values [which might suggest 
the need for something like "ARCH / GARCH" (autoregressive conditional 
heteroscedasticity)?  I mention this because you talk about 
"'unexpected' shocks at especific points in time".  If these "shocks" 
can be explained by some other variable, then you don't need ARCH / 
GARCH.  However, if the sources can not be reasonably modeled from other 
variables, then you might need ARCH / GARCH.]

	  hope this helps.
	  spencer graves

Antonio Revilla wrote:

> Dear list members,
> 
> I am facing a 3-level model, for which my research hypotheses suggest that 
> the variance of both level-1 and level-2 residuals may be a function of a 
> level-3 variable.
> 
> To be a bit more clear: I am fitting a longitudinal model for a panel of 
> companies grouped in industries. I suggest that some industry variables may 
> create 'unexpected' shocks at especific points in time; such shocks are not 
> accounted for by the explanatory variables in the model, so that they will 
> presumably increase variance of level-1 residuals. On the other hand, 
> industry-level attributes may also affect the relative relative size of 
> firm-level permanent effects (represented by level-2 residuals)
> 
> Do you know how could I model such a residual structure in R? I have been 
> looking at the varfunc command in the nlme package, but I am not sure if 
> such a function can perform the kind of analysis I actually need.
> 
> Thank you very much in advance,
> 
> Antonio
> 
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