Forum: help

RE: response variable & random effects in censReg [ Reply ] By: Arne Henningsen on 2017-05-06 06:08	[forum:45117]
You can use the 'Delta Method' to calculate (approximate) standard errors of sigmaMu and sigmaNu: https://en.wikipedia.org/wiki/Delta_method

RE: response variable & random effects in censReg [ Reply ] By: E Hunt on 2017-05-05 19:51	[forum:45116]
Thanks Arne - that's helpful - so one final question, can one transform the standard errors for logSigmaMu and logSigmaNu in the same way using exp() or is there more to it than that?

RE: response variable & random effects in censReg [ Reply ]
By: Arne Henningsen on 2017-05-04 09:07

[forum:45115]

You can calculate the (estimated) variances of mu (the individual-specific effects) and nu (which absorbs the remaining unexplained effects) by applying the exponential function to the estimates of 'logSigmaMu' and 'logSigmaNu', respectively. Does this answer your question? (I don't know the lmer package and the attached figure does not seem to be a screenshot). Please note that--for historical reasons--econometricians and statisticians in natural scientists use the term 'random effects' in different ways. So please take a look at the 'vignette' of the 'censReg' package and make sure that you indeed estimate the random effects model that you intend to estimate.

RE: response variable & random effects in censReg [ Reply ] By: E Hunt on 2017-05-03 21:08	[forum:45113] Screen Shot 2017-05-03 at 13.57.54.png (18) downloads
Dear Arne, Thank you very much for your replies. All very useful. May I add one follow-up question: can censReg report the variance explained by the individual-specific random effects, and the residual variance, as in for instance the lmer package (see attached example)? Thank you

RE: response variable & random effects in censReg [ Reply ]
By: Arne Henningsen on 2017-04-16 05:49

[forum:45095]

1) Theoretically, the distribution of the dependent variable is irrelevant but in standard censored regression models, it is assumed that the error term follows a normal / Gaussian distribution. However, in practice, the distribution of the error term is often similar to the distribution of the dependent variable so that a symmetric Gaussian-like distribution of the dependent variable (without fat tails) often implies a symmetric Gaussian-like distribution distribution of the error term. Hence, if your dependent variable has a symmetric Gaussian-like distribution (except for the censoring), I suggest to keep it as it is. if your dependent variable has a very skewed distribution (perhaps with a fat tail), I suggest that you transform it to make the distribution more Gaussian-like.

2) What do you mean by "include time as a fixed effect"? Did you include 5 dummy variables for 5 of the 6 years as additional explanatory variables? Alternatively, you could include a linear, quadratic, logarithmic, exponential and/or another time trend as explanatory variable(s) and then test this more parsimonious specification against the specification with the time dummies. If time has a statistically significant effect, you need to take this into account in your analysis.

3) The statistical significance of logSigmaMu and logSigmaNu is usually irrelevant. If you take the logarithm of the dependent variable, sigma_mu does not significantly differ from 1, while sigma_mu does significantly differ from one. If you do not take the logarithm of the dependent variable, both sigma_mu and sigma_nu significantly differ from one. This is usually not very informative -- and does not affect the interpretation of the other estimated parameters and their statistical significance.

4) I am not sure about this.

response variable & random effects in censReg [ Reply ]
By: E Hunt on 2017-04-15 07:45

[forum:45094]

Hello,

I have 24 'cross-sectional' observations (i = 1, ..., 24) and 6 time observations (t = 1, ..., 6). My dependent variable is attack speed (time). This is right-censored at a maximum of 600s to attack. I have some brief questions about censReg:

1) are there any distributional expectations on the dependent variable (DV)? For instance with a GLMM we would prefer the DV to be normally distributed. If I take a log transform of my DV it is more normal. Should I? I suppose it is better not to, if not necessary, because the estimated coefficients have a natural interpretation without it.

2) At face value, there is an effect of time in my DV: attack times seem to get longer as t goes 1...6. However, if I include time as a fixed effect, the parameters of interest in my model are no longer significant. I was wondering whether the random effects included when censReg works with pdata.frame are sufficient in themselves to say 'time has been included as a random effect', since the nu_it term is time-dependent?

3) How do I interpret the significance (or not) of the terms logSigmaMu and logSigmaNu? If I log the DV, logSigmaMu is not significant (p=0.66) but logSigmaNu is (p=5x10^-6). If I do not log the DV, both are highly significant (p<2x10^-16). What is the correct way to report these results, and how do they affect my conclusions of interest regarding the other parameters in the model? Put differently, if these two terms are significant, does that undermine my conclusions regarding other significant parameters?

4) are there any tests for goodness of fit for censReg models? e.g. in GLMMs we want normality in the Pearson residuals. What can I report in my write-up to give confidence that the model is a good fit?

Many thanks for your advice