5

Two points: Your data are log-log scaled. So why don't you take the logs of them? Since you expect a sigmoid function behind the data, why not trying fitting it to the data? Below, I model your log-transformed data as a (scaled) difference of two softplus functions, $y = log(1+e^x)$, plus a constant term: $$ y = log(1 + e^{\alpha_1 + \beta x}) - log(1 + e^...


3

I have nothing to add to whuber's brilliant answer using the Box-Cox transformation. I just wanted to offer an alternative source of the approximation, using the Maclaurin series for the natural logarithm: $$\ln (y+1) = y - \frac{y^2}{2} + \frac{y^3}{3} - \cdots.$$ Ignoring the higher-order terms in the expansion gives the crude first-order approximation: ...


2

If the response is count valued, you should consider using an appropriate modeling strategy that implicitly log-transforms the intensity rather than the count values themselves. Consider that a Poisson process with low intensity is likely to have right skewed results and many 0s, but log-transforms of the data would lead to highly biased estimates of the ...


2

You can just run as.data.frame() on the sempreds object to turn it into a data.frame. Note that this isn't actually prediction; you're estimating factor scores. This covered in any SEM textbook (e.g., Bollen 1989). Factor scores are imperfect estimates of the latent variable that can often be used in subsequent analyses or for descriptive purposes. That ...


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