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The best solution to this problem is to try extremely hard to avoid having missing data in the first place. When there are missing values that are impossible or too costly to avoid, one approach is to replace the missing values with plausible estimates, known as imputation. Another easier approach is to consider only models that contain predictors with no or few missing values.
This may be unsatisfactory, however, because even a predictor variable with a large number of missing values can contain useful information. In small datasets, a lack of observations can lead to poorly estimated models with large standard errors. Such models are said to lack statistical power because there is insufficient data to be able to detect significant associations between the response and predictors. So, how much data do we need to conduct a successful regression analysis?
A common rule of thumb is that 10 data observations per predictor variable is a pragmatic lower bound for sample size. However, it is not so much the number of data observations that determines whether a regression model is going to be useful, but rather whether the resulting model satisfies the LINE conditions. In some circumstances, a model applied to fewer than 10 data observations per predictor variable might be perfectly fine if, say, the model fits the data really well and the LINE conditions seem fine , while in other circumstances a model applied to a few hundred data points per predictor variable might be pretty poor if, say, the model fits the data badly and one or more conditions are seriously violated.
However, it is difficult to say exactly how much data would be needed. It is possible that we could adequately model interaction with a relatively small number of observations if the interaction effect was pronounced and there was little statistical error. Conversely, in datasets with only weak interaction effects and relatively large statistical error, it might take a much larger number of observations to have a satisfactory model. In practice, we have methods for assessing the LINE conditions, so it is possible to consider whether an interaction model approximately satisfies the assumptions on a case-by-case basis.
From a different perspective, if we are designing a study and need to know how much data to collect, then we need to get into sample size and power calculations, which rapidly become quite complex. Frank Harrell is an active member of this site. So i hope this question gets his attention and we can then hear directly from him. One scenario would be that all your parameters have about the same estimated magnitude of effect, but their uncertainties vary so that some are significant and others are not.
You definitely don't want to conclude in this case that "variables A and B are important, variables C, D, and E are not". The CIs will give you this information. Show 2 more comments. Michael R.
Chernick Michael R. Chernick I added my correlation matrix. Do you think with this correlation matrix doing regression is reasonable? Just I want to find any possible relation between independent variables and dependent variable. The estimates will probably have large variance and so statitical significance should not be the focus.
Ypu could look at regression diagnostics for collinearity. That might help. But I would recommend looking at a variety of subset models to see how the fit changes and which combinations of variables seem to do well and do poorly. I really think bootstrapping the data will show you something about the stability of the choice of predictors. I think you just want to see if there is one or two variables that seem to stand head a shoulders above the rest.
But you may nit find anything. Since there is some correlation between these predictors, presumably their estimated coefficients are "worth" less than 1 degree of freedom. And what about, say, regression splines or other local regression: do we have to account for the fact that only a subset of observations is used in construction of the components?
And if we use a kernel to apply weights to predictors, does that affect the effective number of observations used? Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta.
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