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Tristan
Tristan
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All the answers so far seem to miss a very basic point: the functional form you choose should be flexible enough to capture the features that are scientifically relevant. Models 2-5 impose zero coefficients on some terms without scientific justification. And even if scientifically justified, Model 1 remains appealing because you might as well test for the zero coefficients rather than impose them.

TheyThe key is understanding what the restrictions mean. The typical admonition to avoid Models 3-5 is because in most applications the assumptions they impose are scientifically implausible. Model 3 assumes X2 only influences the slope dY/dX1 but not the level. Model 4 assumes X1 only influences the slope dY/dX2 but not the level. And Model 5 assumes neither X1 nor X2 affects the level, but only dY/dX1 or dY/dX2. In most applications these assumptions don't seem reasonable. Model 2 also imposes a zero coefficient but still has some merit. It gives the best linear approximation to the data, which in many cases satisfies the scientific goal.

All the answers so far seem to miss a very basic point: the functional form you choose should be flexible enough to capture the features that are scientifically relevant. Models 2-5 impose zero coefficients on some terms without scientific justification. And even if scientifically justified, Model 1 remains appealing because you might as well test for the zero coefficients rather than impose them.

They key is understanding what the restrictions mean. The typical admonition to avoid Models 3-5 is because in most applications the assumptions they impose are scientifically implausible. Model 3 assumes X2 only influences the slope dY/dX1 but not the level. Model 4 assumes X1 only influences the slope dY/dX2 but not the level. And Model 5 assumes neither X1 nor X2 affects the level, but only dY/dX1 or dY/dX2. In most applications these assumptions don't seem reasonable. Model 2 also imposes a zero coefficient but still has some merit. It gives the best linear approximation to the data, which in many cases satisfies the scientific goal.

All the answers so far seem to miss a very basic point: the functional form you choose should be flexible enough to capture the features that are scientifically relevant. Models 2-5 impose zero coefficients on some terms without scientific justification. And even if scientifically justified, Model 1 remains appealing because you might as well test for the zero coefficients rather than impose them.

The key is understanding what the restrictions mean. The typical admonition to avoid Models 3-5 is because in most applications the assumptions they impose are scientifically implausible. Model 3 assumes X2 only influences the slope dY/dX1 but not the level. Model 4 assumes X1 only influences the slope dY/dX2 but not the level. And Model 5 assumes neither X1 nor X2 affects the level, but only dY/dX1 or dY/dX2. In most applications these assumptions don't seem reasonable. Model 2 also imposes a zero coefficient but still has some merit. It gives the best linear approximation to the data, which in many cases satisfies the scientific goal.

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Tristan
Tristan
  • 1.7k
  • 11
  • 12

All the answers so far seem to miss a very basic point: the functional form you choose should be flexible enough to capture the features that are scientifically relevant. Models 2-5 impose zero coefficients on some terms without scientific justification. And even if scientifically justified, Model 1 remains appealing because you might as well test for the zero coefficients rather than impose them.

They key is understanding what the restrictions mean. The typical admonition to avoid Models 3-5 is because in most applications the assumptions they impose are scientifically implausible. Model 3 assumes X2 only influences the slope dY/dX1 but not the level. Model 4 assumes X1 only influences the slope dY/dX2 but not the level. And Model 5 assumes neither X1 nor X2 affects the level, but only dY/dX1 or dY/dX2. In most applications these assumptions don't seem reasonable. Model 2 also imposes a zero coefficient but still has some merit. It gives the best linear approximation to the data, which in many cases satisfies the scientific goal.