I would like to run a study in which my predictor is a continuous variable. I already know that the distribution is normal but most of the points fall close to the center. I think that small differences in the scores of this predictor are not very meaningful. I thus expect that using this predictor continuously in a linear mixed model design might drastically decrease my power to find an effect. I was wondering if there are alternative statistical methods that can better take this into account and enable me to analyse my data.
Best,
Martina
It sounds to me like you aer doing several things:
1. predictor is a continuous variable-predictors are supposed to be fixed i.e. measured without error:see: https://www.amazon.com/Applied-Linear-Statistical-Models-2013/dp/1259064743/ref=sr_1_1?crid=1OOICPVJLONI5&keywords=applied+linear+statistical+models+5th+edition&qid=1579892525&sprefix=Applied+linear%2Caps%2C160&sr=8-1
If this assumption is violated you need an errors in variables model: See: https://en.wikipedia.org/wiki/Errors-in-variables_models
2. It sounds like you are choosing your model based on what you expect to find:
"decrease my power to find an effect"-you already used in correct reasoning here, see point 1.
3. To answer your direct question see point 1. errors in variables models ref. This is the thing to do. Best wishes, David Booth
Yes, non varying predictors lack power to detect effects. In general this is a design issue rather than an analytical one.
On what basis do you think it is not varying ; what is its coefficient of variation? That is a dimensionless measure. If you multiplied your X by a100 it would look more variable but the cv would be the same. However, You would know better than me what is meaningful variation In the X.
Kelvyn Jones I don't follow what you mean by "non-varying predictors lack power to predict effects." I would agree with you if you meant essentially constant columns but since the question says "continuous" I know not what to do except what I suggested. Please help. Thanks, David
Dear Martina,
What statistical method you want to implement? and for what type of data?
If you using model based predictive models, also please mention weather you using parametric or non parametric distribution model? I think if you clarify your questions, you will get helpful answers.
David Eugene Booth Sorry, my point was if a predictor (I habitually use that term for what others call an explanatory variable) has a relative small standard deviation then the Standard error of the associated coefficient estimate will be large; hence low power. I do not necessarily see this as a measurement error thing as the variable may be precisely and accurately measured but in the achieved sample, there is little variation. My teaching example is the relation between response of house price and predictor of size; if sample is all 3 bedroom houses then you will not be able to estimate a relation as there is no variation in the X at all. You need to sample areas with different size houses - you have to use your geographical imagination to sample purposely.
Multilevel models can help here as they estimate precision-weighted relations and they can borrow strength (Tukey's term) for many different places and can even estimate a slope for a place even if that place does only have 3 bedroom houses. See Article Do multilevel models ever give different results?.
The famous example is: Article Using Empirical Bayes Techniques in the Law School Validity Studies
which pools information across law schools ; the problem there is that each school has a narrow range of the predictor variable, ability on intake.
Of course you can use full Bayes and include a parameter for measurement error as in the MCMC chapter here
Book Developing multilevel models for analysing contextuality, he...
But I think that attention is also needed to sample design in these situations.
Hi all,
thanks a lot for all your answers.
I agree it is not a measurement error. We generally find few individuals with a score at the extremes of the continous predictor. As a design strategy, I can either test participants at the extremes or treat the variable as continous, which is associated with the problems we are discussing. However, considering only the extremes would reduce my power as well because most probably I would not be able to achieve large sample sizes. Thank you in advance for all your feedback.
The variability is a relative thing. so could you give us the calculated coefficient of variation of the exposure variable? I am not suggesting that you only go for extremes but that you obtain data throughout the possible range of X if you can control what you are measuring.
Kelvyn Jones Thank you so much for your reply. I agree it is a design issue. But in my experience with this sort of thing ( business and economic modeling) errors of in variable models are almost completely ignored when they should not be. In this case, I would defer to subject matter specialists who are undoubtedly better positioned than I to know the ins and outs of their data. Thank you very much. David
HI thank you for your responses. in the article Article Time dependent effects of stress prior to encoding on event-...
, they write: "Mean intra- and inter-assay coefficients of variation are typically less than 5%, and the lower and upper detection limits were 0.015 mg/dl (0.41 nmol/l) and 4.0 mg/dl (110.4 nmol/l), respectively. "
Will try and scan the article later , but I notice that there is a 4.0/0.015 = 276fold range in the extremes, which is pretty large, it is not as if its is 0.045/0.015!
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