I have 10 responses and 20 predictors for which I measured values in two conditions. I ran elastic model for each response at each condition separately. As a result, I will have two association networks between responses and predictors, each for one condition. I then need to statistically compare the two association networks (edges are weighted based on the regression coefficients obtained by elastic net regression between a predictor and a response). I need to know whether the association between a response A and a regressor B in condition 1 is significantly different from the association between A and B in condition 2. Could you maybe help me which kind of test I can use? Thanks!
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$\begingroup$ So the predictors were measured at two time points , but the response remained the same? $\endgroup$– JanoschCommented Jan 17, 2020 at 10:22
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$\begingroup$ Not really! the predictors and responses measured at the same time points, but in two different conditions, in control and in salt. $\endgroup$– sbmmCommented Jan 17, 2020 at 12:18
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$\begingroup$ so overall you recorded 20. 10 in control and 10 in salt $\endgroup$– JanoschCommented Jan 17, 2020 at 13:47
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$\begingroup$ actually 20 predictors were measured at 10 time points in condition one, and the same 20 predictors were measured at 10 times points in condition two. $\endgroup$– sbmmCommented Jan 17, 2020 at 14:28
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Given that the response in the control group are independent of the one in the experimental group you could try to fit just a single model. And you include control/experimental as a variable and include the interaction with the 20 predictors and the newly added variable. Significant interaction would mean difference in effect of the predictor between the groups.
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$\begingroup$ This looks like a good approach, but it begs the question of testing significance of coefficients in an Elastic Net model: do you have any ideas how to do that effectively? $\endgroup$– whuber ♦Commented Jan 17, 2020 at 13:53
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$\begingroup$ I believe the same as whuber. and the responses are the same variable, but just measured in two different conditions. $\endgroup$– sbmmCommented Jan 17, 2020 at 14:31