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  • Negative log likelihood

    Hi Everyone,

    I am running an ARDL - ECM on time series data containing continuous variables. 3 of my variables are ratios (fdi, emissions and trade openness). The log likelihood when I log transform the ratios is positive. When I run the regressions without transforming the variables into logs its negative

    I have read that ratios do not have to be converted to log form. In this regard, does the negative log likelihood make my results invalid or say that the estimations are not of great quality?

    Should I run regressions in log form or just maintain ratios

    Thanks

  • #2
    The likelihood is a product (of probability densities or of probabilities, as fits the case) and the log likelihood equivalently is a sum. A density above 1 (in the units of measurement you are using; a probability above 1 is impossible) implies a positive logarithm and if that is typical the overall log likelihood will be positive.

    Very likely the range of your logarithm variables is less than 1. It follows necessarily that on average the density must be above 1, as the density must integrate to 1 over the entire distribution.

    All is well with your results. There is nothing to fix there.

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    • #3
      Thanks Nick!!!

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      • #4
        That said, whether ratios or log ratios are better for your purpose is quite impossible to judge. I have a bias to logging ratios but that can be impossible or a bad idea too.

        Also, the density concerned is that of the response variable, so that is key here.

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