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Look, I am 100% for the conclusion that we should not as a default case have people working too much! Even a 40 hour work week, for work that is statistically u

Look, I am 100% for the conclusion that we should not as a default case have people working too much! Even a 40 hour work week, for work that is statistically usual today, is in my opinion inhumane. That philosophical belief however does not win out in the context of this particular analysis. My agenda is to support sensible discourse on the question of how our brains adapt and how we live, using rigorous thought. Maybe I'm not seeing the problem with my reasoning but it seems pretty clear to me. The problem is that you automatically get an upward or downward parabola, plotting cognitive scores versus working hours, if you have a non-zero coefficient in working hours^2 It's very unlikely that you'll get an upward parabola, especially given the strong anticorrelation between unemployment and cognitive scores that they use. In science, you have a judgment call for which predictors you plug into the statistical analysis. Choosing any particular function, be it working hours^2, sin(working hours/100), or even, say, ballmerpeak(alcohol content) will effect the statistical results in factor analysis or anything else. Since we chose only linear and quadratic functions to get coefficients for in our statistical analysis, the functions are going to be a parabola -- either up or down.

xapata 10y ago
The coefficient for the squared component could easily be zero. This is called "not statistically significant". There is no guarantee for a parabolic shape.
- DaniFong 10y ago
  The measure of possible data sets where, by standard statistical analysis, the coefficient for the squared component is zero, is tiny. There's no guarantee for a parabola, just a very high degree of certainty. Your other point, that the parabola could be "not statistically significant," is true. But given a strong degree of significant correlation between unemployment and the cognitive indicators, even if the dependence is totally flat for the cognitive indicators between 5 hours worked and 100 hours worked, you will still get a parabola by this method of statistical analysis. Do not forget, this is model fitting.
  - xapata 10y ago
    > is zero Sigh. No coefficient is ever exactly zero, just very close [0]. I didn't think I needed to explain that when writing, "could be zero." > you will still get a parabola If the squared parameter is not statistically significant, the author will likely drop it from the model. In that case, we would not see a parabolic model and the paper wouldn't exist. The authors would have moved on to a different topic, or found a different dataset. If the coefficient is so small that it is indistinguishable from zero (not significant), then we ignore the associated variable entirely. To do otherwise would require us to discuss an infinity of possible variables as if they mattered to the model. > correlation between unemployment and cognitive indicators If you're arguing that the author should have dropped all observations of unemployed persons from the dataset, that's completely separate and has nothing to do with parabolas. [0] "ever" loosely defined.
psychometry 10y ago
"The functions are going to be a parabola." What functions? A plot of which two variables? I have no idea what you're talking about and I'm a grad student in biostats.
- DaniFong 10y ago
  I'm sorry, I am trying to explain something that is very clear in my head, and I'm pretty sure that I'm right, but I haven't had bio-stats training specifically so I do not know the language precisely. My background is in physics, computer science, and epistemology. The functions I am referring to are estimators of cognitive indicators (like backwards digit span, say, that they use in the paper), as a function of working hours. Take a look at page 21 for some plots. For each of the cognitive indicators, the estimator is a downwards parabola as a function of working hours. What I am saying is that this is an artifact of the analysis. The shape could be far different -- in fact it could be a bad case of curve fitting. Additionally -- why not just directly plot the data as a scatter plot or a binned average of cognitive indicators for bins between, say, 20 - 25 hours, 25 - 30 hours, etc? Then at least we could see if the parabolas are close to the data... https://www.melbourneinstitute.com/downloads/working_paper_series/wp2016n07.pdf https://www.melbourneinstitute.com/downloads/working_paper_s...
  - psychometry 10y ago
    There's nothing wrong with the inclusion of a quadratic term in a linear model if the variable is significant, which is clearly is according to Table IV. You can't just plot a single predictor against the sample outcome and expect the plot to be particularly revealing in multiple regression. Plus, this isn't even multiple regression; this is a two-stage least squares multiple regression. The working hour (WH) variables are instruments, not predictors. See page 6. Instrumental variables exist specifically to deal with the case of a possible bidirectional causal association between predictor and response.
    - DaniFong 10y ago
      I'm afraid I don't think you are understanding my point, but apparently it is a difficult one to make. I'm unfortunately too busy to make it clearer, so I will just leave you with a koan. Why not include a third order term in the regression? What about an n-th order term? What assumptions do we "bake into" the results of a statistical regression as an effect of including, or not, any function on the original data? The statistical significance of the quadratic term is actually dependent upon the presence of any more complex or higher order terms in the regression, just as the coefficients and the statistics of the linear term will depend on the presence of the second order term in the analysis. I'm not saying you should never include a quadratic term in a regression, I'm saying we should understand what the regression is doing when it is fitting a model.

xapata 10y ago

The coefficient for the squared component could easily be zero. This is called "not statistically significant". There is no guarantee for a parabolic shape.

DaniFong 10y ago
The measure of possible data sets where, by standard statistical analysis, the coefficient for the squared component is zero, is tiny. There's no guarantee for a parabola, just a very high degree of certainty. Your other point, that the parabola could be "not statistically significant," is true. But given a strong degree of significant correlation between unemployment and the cognitive indicators, even if the dependence is totally flat for the cognitive indicators between 5 hours worked and 100 hours worked, you will still get a parabola by this method of statistical analysis. Do not forget, this is model fitting.
- xapata 10y ago
  > is zero Sigh. No coefficient is ever exactly zero, just very close [0]. I didn't think I needed to explain that when writing, "could be zero." > you will still get a parabola If the squared parameter is not statistically significant, the author will likely drop it from the model. In that case, we would not see a parabolic model and the paper wouldn't exist. The authors would have moved on to a different topic, or found a different dataset. If the coefficient is so small that it is indistinguishable from zero (not significant), then we ignore the associated variable entirely. To do otherwise would require us to discuss an infinity of possible variables as if they mattered to the model. > correlation between unemployment and cognitive indicators If you're arguing that the author should have dropped all observations of unemployed persons from the dataset, that's completely separate and has nothing to do with parabolas. [0] "ever" loosely defined.

psychometry 10y ago

"The functions are going to be a parabola." What functions? A plot of which two variables? I have no idea what you're talking about and I'm a grad student in biostats.

DaniFong 10y ago
I'm sorry, I am trying to explain something that is very clear in my head, and I'm pretty sure that I'm right, but I haven't had bio-stats training specifically so I do not know the language precisely. My background is in physics, computer science, and epistemology. The functions I am referring to are estimators of cognitive indicators (like backwards digit span, say, that they use in the paper), as a function of working hours. Take a look at page 21 for some plots. For each of the cognitive indicators, the estimator is a downwards parabola as a function of working hours. What I am saying is that this is an artifact of the analysis. The shape could be far different -- in fact it could be a bad case of curve fitting. Additionally -- why not just directly plot the data as a scatter plot or a binned average of cognitive indicators for bins between, say, 20 - 25 hours, 25 - 30 hours, etc? Then at least we could see if the parabolas are close to the data... https://www.melbourneinstitute.com/downloads/working_paper_series/wp2016n07.pdf https://www.melbourneinstitute.com/downloads/working_paper_s...
- psychometry 10y ago
  There's nothing wrong with the inclusion of a quadratic term in a linear model if the variable is significant, which is clearly is according to Table IV. You can't just plot a single predictor against the sample outcome and expect the plot to be particularly revealing in multiple regression. Plus, this isn't even multiple regression; this is a two-stage least squares multiple regression. The working hour (WH) variables are instruments, not predictors. See page 6. Instrumental variables exist specifically to deal with the case of a possible bidirectional causal association between predictor and response.
  - DaniFong 10y ago
    I'm afraid I don't think you are understanding my point, but apparently it is a difficult one to make. I'm unfortunately too busy to make it clearer, so I will just leave you with a koan. Why not include a third order term in the regression? What about an n-th order term? What assumptions do we "bake into" the results of a statistical regression as an effect of including, or not, any function on the original data? The statistical significance of the quadratic term is actually dependent upon the presence of any more complex or higher order terms in the regression, just as the coefficients and the statistics of the linear term will depend on the presence of the second order term in the analysis. I'm not saying you should never include a quadratic term in a regression, I'm saying we should understand what the regression is doing when it is fitting a model.