Hello OpenMx community,
I am trying to compute confidence intervals for the parameters that I define as matrix algebra
summary(model) gives the following (only CIs showing):
confidence intervals: lbound estimate ubound note ACE.Variance_components[1,1] NA 6.601569e-01 NA !!! ACE.Variance_components[2,1] NA 3.638004e-01 NA !!! ACE.Variance_components[3,1] NA 7.779408e-01 NA !!! ACE.Variance_components[4,1] NA 3.401663e-01 NA !!! ACE.Variance_components[5,1] NA 3.728521e-01 NA !!! ACE.Variance_components[6,1] NA 5.272372e-01 NA !!! ACE.Variance_components[7,1] NA 6.268351e-01 NA !!! ACE.Variance_components[8,1] NA 4.262247e-01 NA !!!
summary(model, verbose = TRUE) gives the following output (also truncated):
CI details: parameter side value fit diagnostic statusCode method ACE.mean[1,1] 1 ACE.Variance_components[1,1] lower 0.6308384 342452.3 active box constraint OK neale-miller-1997 -0.005694432 2 ACE.Variance_components[1,1] upper 0.6893814 342452.3 active box constraint OK neale-miller-1997 -0.005786365 3 ACE.Variance_components[2,1] lower 0.3225724 342452.3 active box constraint OK neale-miller-1997 -0.005760040 4 ACE.Variance_components[2,1] upper 0.4051682 342452.3 active box constraint OK neale-miller-1997 -0.005729072 5 ACE.Variance_components[3,1] lower 0.7592378 342452.3 active box constraint OK neale-miller-1997 -0.005746466 6 ACE.Variance_components[3,1] upper 0.7939006 342452.3 active box constraint OK neale-miller-1997 -0.005738854 7 ACE.Variance_components[4,1] lower 0.3079076 342452.3 active box constraint OK neale-miller-1997 -0.005746881 8 ACE.Variance_components[4,1] upper 0.3735943 342452.3 active box constraint OK neale-miller-1997 -0.005738552 9 ACE.Variance_components[5,1] lower 0.3407635 342452.3 active box constraint OK neale-miller-1997 -0.005762424 10 ACE.Variance_components[5,1] upper 0.3928472 349204.8 alpha level not reached OK neale-miller-1997 -0.005742996
My questions are:
1) Can I use the intervals that have status OK or OK/green?
2) Is there some documentation that explains the status codes of CIs?
Thank you,
Ivan
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You probably shouldn't. While it's true that the optimizer's status code is "OK", the diagnostic is telling you that there are active box constraints at the solutions of the confidence-limit searches, meaning that the confidence intervals may be wrong because they are too narrow. That's why the limits are reported as
NAin the vanillasummary()output. Getting rid of unnecessary lbounds in yourmxMatrix()calls might resolve the issue. Also, if you're not currently using SLSQP as the optimizer, try switching to it.Yes. The optimizer status codes you're seeing in the verbose
summary()output have the same meaning as they always do.See the man page for
as.statusCode().Thank you, this is very helpful.
Do SE's suffer from this in the same way?
No. SEs are a function of the second partial derivatives of the loglikelihood at the ML solution, and do not require additional searches by the optimizer. However, confidence intervals calculated from SEs do not have the attractive theoretical properties that profile-likelihood confidence intervals do. Specifically, profile-likelihood confidence intervals (1) respect constraints on the parameter space, (2) are not necessarily symmetric around the point estimate, and (3) are invariant under transformation of the parameter.
If you're going to form confidence intervals from the SEs, you should at least get robust SEs first, from
imxRobustSE().