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tl;dr I'm not sure your objective function makes sense, my guess is that you have a typo. (Furthermore, if your objective function is working with mle, you don't need to set fixed explicitly: the profile method will automatically compute likelihood profiles for you ...)

Let's start with the full model, and let's use optim() rather than stats4::mle() (I know you want to get back to mle so that you can do likelihood profiling, but it's a little bit easier to debug optim() problems since there is one less layer of code to dig through.)

Since optim() wants an objective function that takes a vector rather than a list of arguments, write a wrapper (we could also use do.call(fr, as.list(p))):

logLik evaluates the log-likelihood at the maximum-likelihood estimates of the parameters. The maximum-likelihood estimates of the coefficients are the same as the least-squares estimates, but the denominator of the maximum-likelihood estimate of the variance is n, while summary(mod_lm)$sigma is the squared-root of the unbiased estimate of the variance, whose denominator is the degrees of freedom, here n-1. So you get the same results if you do:

That does appear to be a bug. I've fixed it in the latest development version. These can be obtained by going to https://github.com/statnet/ergm and https://github.com/statnet/ergm.count and either using install_github() or downloading the binaries found in the README. Note, also that, the blockdiag() constraint has been provisionally moved to https://github.com/statnet/tergm .

How about using a list of data.frames and then rbindlist them (a data.table function)

There are a bunch of issues here. The primary one is that your likelihood expression is wrong (you can't log the components separately and then add them, you have to add the components and then take the log). Your bounds are also funny: the mixture probability should be [0,1] and the means should be [0, Inf].

The other problem you have is that with the current simulation design (n=20, prob=0.01), you have a high probability of getting no points in the first mixture component (the probability of a point being in the second component is 1-0.01=0.99, so the probability that all of the points are in the second component is 0.99^20 = 82%). In this case the MLE will be degenerate (i.e., you're trying to fit a two-component mixture to a data set that essentially only has one component); in this case any of these solutions will give equivalent likelihoods:

• prob=0, mu2=mean of the data, mu1=anything
• prob=1, mu1=mean of the data, mu2=anything
• mu1=mu2=mean of the data, prob=anything

With all these solutions, where you end up will depend very sensitively on starting conditions and optimization algorithm.

For this problem I would encourage you to use the built-in dmixexp2 function from the Renext package (which correctly implements the log-likelihood as log(p*Prob(X|exp1) + (1-p)*Prob(X|exp2))) and the formula interface to mle2:

There are two problems. (1) the Rayleigh distribution does not seem to be a good fit to the data (see plot output below) and (2) you need a better starting value. Since sigma is proportional to the mean for the Rayleigh distribution (see wikipedia) try that:

The discrepancy is mainly due to the differing pdfs.

In python st.pareto.fit() uses a Pareto distribution defined via this pdf:

The difference appears to be the result of the default relative tolerances used by the optimizers (and normal floating point imprecision). If you tighten the tolerance in the R calculation, the result is closer to the SciPy result:

Since you want to save the data into a data frame I will assume you want jj to contain the result. As your code stands you probably want to do something like: