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If willpower is the strongest indicator for income then controlling for parent’s income leads to some strange circular reasoning: willpower is not a strong infl

If willpower is the strongest indicator for income then controlling for parent’s income leads to some strange circular reasoning: willpower is not a strong influence of income when controlling for income.

ethbro 8y ago
* Above is true, if and only if: - Willpower is non-socially inherited - Willpower is proportionally developed (to their final amount) in children at the time of testing I would assume the hypothesis of the researchers was that children were more tabula rasa at the age tested, and therefore controlling for variables wouldn't be circular.
- xapata 8y ago
  That's not the issue. Controlling for a variable is a model like `y ~ x + z` where x is the explanatory variable and z is the control. The commenter complained that since `y ~ z` and `x ~ z` the interpretation of the effect is strange. Not so. This is the sole purpose of controlling for confounders. If parents income were either not correlated with willpower or child's income, it could be dropped from the model. The stronger the correlation of x and z, the more important the control.
  - eanzenberg 8y ago
    If x and z are strongly correlated you can't determine causality for either within linear models. They are practically interchangeable and removing one will not decrease the effect of the other. "Controlling for", or keeping both on the right side, will decrease the effect of one over the other in unexpected ways, and why strong collinearity yields strange results in linear models.
    - xapata 8y ago
      If multicollinearity were such an issue, you'd be rejecting a wide range of techniques, such as including a lag term as a regressor for autoregressive models. In fact, you could consider this situation as an autoregressive process, using generations instead of traditional time steps.
      - mlthoughts2018 8y ago
        Multicollinearity is a huge issue when fitting autoregressive and distributed lag models. In fact, it is even mentioned as such in the introduction section of the Wikipedia article on distributed lag [0]. Imagine a second order autoregression model for a time series that is a flat constant value for all time. How would you assign the coefficient for the first lag term and the second lag term? 0.5 to both? 1.0 to one and 0.0 to the other? In the presence of perfect correlation like that, it would be indeterminate how to assign effect sizes. Prediction accuracy of the model might be fine, but any causal interpretation of the effect sizes would be nonsense. This also happens greatly for lagged regressors for more standard regression problems, and you often have to do something like z-scoring them and then combining the correlated regressions together into some type of pre-treatment aggregate score, like an average... effectively reducing N correlated lag terms into 1 composite score, when the correlations are high enough to cause multicollinearity problems. [1] has some further details. In the context of pure forecast accuracy, you may not care so much about multicollinearity as long as the overall prediction is highly accurate. But since this comment thread was about causality, I think it's important to point it out here. It can cause problems for causal inference in many classes of models, and it is a reason why you have to do careful pre-treatments, instrumental variable methods, etc., in some cases. [0] < https://en.wikipedia.org/wiki/Distributed_lag https://en.wikipedia.org/wiki/Distributed_lag > [1] < https://stats.stackexchange.com/a/278049/8927 https://stats.stackexchange.com/a/278049/8927 >
        xapata 8y ago
        Those are good points. Your initial comment criticized the endogeneity issue, not the multicollinearity. Further, controlling for parents income is essentially an AR1 model, which doesn't suffer from the multicollinearity interpretation issues you described. The problem would be if child willpower were too highly correlated with parents' income, not if parents' income were highly correlated with child's income.
deleted 8y ago
[deleted]
xapata 8y ago
No, you've forgotten that there are two incomes in question, parents and child. Parents' income and child's willpower are both correlated with child's income and each other.
- eanzenberg 8y ago
  I think it's already well proven that parents' income is highly correlated with childrens' income, for a variety of reasons. It's pretty safe to use them interchangeably
  - xapata 8y ago
    Not if you're trying to identify the effect of a child's willpower on the child's future income. Gotta control for those confounders and prevent endogeneity.

ethbro 8y ago

* Above is true, if and only if: - Willpower is non-socially inherited - Willpower is proportionally developed (to their final amount) in children at the time of testing I would assume the hypothesis of the researchers was that children were more tabula rasa at the age tested, and therefore controlling for variables wouldn't be circular.

xapata 8y ago
That's not the issue. Controlling for a variable is a model like `y ~ x + z` where x is the explanatory variable and z is the control. The commenter complained that since `y ~ z` and `x ~ z` the interpretation of the effect is strange. Not so. This is the sole purpose of controlling for confounders. If parents income were either not correlated with willpower or child's income, it could be dropped from the model. The stronger the correlation of x and z, the more important the control.
- eanzenberg 8y ago
  If x and z are strongly correlated you can't determine causality for either within linear models. They are practically interchangeable and removing one will not decrease the effect of the other. "Controlling for", or keeping both on the right side, will decrease the effect of one over the other in unexpected ways, and why strong collinearity yields strange results in linear models.
  - xapata 8y ago
    If multicollinearity were such an issue, you'd be rejecting a wide range of techniques, such as including a lag term as a regressor for autoregressive models. In fact, you could consider this situation as an autoregressive process, using generations instead of traditional time steps.
    - mlthoughts2018 8y ago
      Multicollinearity is a huge issue when fitting autoregressive and distributed lag models. In fact, it is even mentioned as such in the introduction section of the Wikipedia article on distributed lag [0]. Imagine a second order autoregression model for a time series that is a flat constant value for all time. How would you assign the coefficient for the first lag term and the second lag term? 0.5 to both? 1.0 to one and 0.0 to the other? In the presence of perfect correlation like that, it would be indeterminate how to assign effect sizes. Prediction accuracy of the model might be fine, but any causal interpretation of the effect sizes would be nonsense. This also happens greatly for lagged regressors for more standard regression problems, and you often have to do something like z-scoring them and then combining the correlated regressions together into some type of pre-treatment aggregate score, like an average... effectively reducing N correlated lag terms into 1 composite score, when the correlations are high enough to cause multicollinearity problems. [1] has some further details. In the context of pure forecast accuracy, you may not care so much about multicollinearity as long as the overall prediction is highly accurate. But since this comment thread was about causality, I think it's important to point it out here. It can cause problems for causal inference in many classes of models, and it is a reason why you have to do careful pre-treatments, instrumental variable methods, etc., in some cases. [0] < https://en.wikipedia.org/wiki/Distributed_lag https://en.wikipedia.org/wiki/Distributed_lag > [1] < https://stats.stackexchange.com/a/278049/8927 https://stats.stackexchange.com/a/278049/8927 >
      - xapata 8y ago
        Those are good points. Your initial comment criticized the endogeneity issue, not the multicollinearity. Further, controlling for parents income is essentially an AR1 model, which doesn't suffer from the multicollinearity interpretation issues you described. The problem would be if child willpower were too highly correlated with parents' income, not if parents' income were highly correlated with child's income.

deleted 8y ago

[deleted]

xapata 8y ago

No, you've forgotten that there are two incomes in question, parents and child. Parents' income and child's willpower are both correlated with child's income and each other.

eanzenberg 8y ago
I think it's already well proven that parents' income is highly correlated with childrens' income, for a variety of reasons. It's pretty safe to use them interchangeably
- xapata 8y ago
  Not if you're trying to identify the effect of a child's willpower on the child's future income. Gotta control for those confounders and prevent endogeneity.