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Added info about code and elaborated on model comparison approach
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Dominik Rolph
Dominik Rolph
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I am working on a multi-level logistic regression model with a binary outcome and a circular predictor. Thanks to this post, I know that I have to add sine and cosine of the circular variable as a predictor and that I can calculate the amplitude $a$ and the phase shift $\phi$ from the regression weights $w_1$ and $w_2$ corresponding to the sine and cosine predictors, respectively.

$a = \sqrt{w_1^2 + w_2^2}$

$\phi = \tan^{-1}\frac{w_1}{w_2}$

Say I am not particularly interested in testing the significance of sine and cosine components individually, which is what the model provides. Instead, I would like to test the overall effect of the circular variable (i. e., the amplitude). My thought was to run a model comparison (in R, anova(m1, m2)) between an intercept-only model m1 and the model including the circular variable m2 to obtain a $\chi^2$ statistic. However, I would like to know if there is a cleaner way of testing the significance of $a$ and $\phi$ - and how the corresponding standard errors are calculated. Thanks in advance for your help!

I am working on a multi-level logistic regression model with a binary outcome and a circular predictor. Thanks to this post, I know that I have to add sine and cosine of the circular variable as a predictor and that I can calculate the amplitude $a$ and the phase shift $\phi$ from the regression weights $w_1$ and $w_2$ corresponding to the sine and cosine predictors, respectively.

$a = \sqrt{w_1^2 + w_2^2}$

$\phi = \tan^{-1}\frac{w_1}{w_2}$

Say I am not particularly interested in testing the significance of sine and cosine components individually, which is what the model provides. Instead, I would like to test the overall effect of the circular variable (i. e., the amplitude). My thought was to run a model comparison between an intercept-only model and the model including the circular variable. However, I would like to know if there is a cleaner way of testing the significance of $a$ and $\phi$ - and how the corresponding standard errors are calculated. Thanks in advance for your help!

I am working on a multi-level logistic regression model with a binary outcome and a circular predictor. Thanks to this post, I know that I have to add sine and cosine of the circular variable as a predictor and that I can calculate the amplitude $a$ and the phase shift $\phi$ from the regression weights $w_1$ and $w_2$ corresponding to the sine and cosine predictors, respectively.

$a = \sqrt{w_1^2 + w_2^2}$

$\phi = \tan^{-1}\frac{w_1}{w_2}$

Say I am not particularly interested in testing the significance of sine and cosine components individually, which is what the model provides. Instead, I would like to test the overall effect of the circular variable (i. e., the amplitude). My thought was to run a model comparison (in R, anova(m1, m2)) between an intercept-only model m1 and the model including the circular variable m2 to obtain a $\chi^2$ statistic. However, I would like to know if there is a cleaner way of testing the significance of $a$ and $\phi$ - and how the corresponding standard errors are calculated. Thanks in advance for your help!

Source Link
Dominik Rolph
Dominik Rolph
  • 23
  • 5

Significance test of the amplitude of sinusoidal regression

I am working on a multi-level logistic regression model with a binary outcome and a circular predictor. Thanks to this post, I know that I have to add sine and cosine of the circular variable as a predictor and that I can calculate the amplitude $a$ and the phase shift $\phi$ from the regression weights $w_1$ and $w_2$ corresponding to the sine and cosine predictors, respectively.

$a = \sqrt{w_1^2 + w_2^2}$

$\phi = \tan^{-1}\frac{w_1}{w_2}$

Say I am not particularly interested in testing the significance of sine and cosine components individually, which is what the model provides. Instead, I would like to test the overall effect of the circular variable (i. e., the amplitude). My thought was to run a model comparison between an intercept-only model and the model including the circular variable. However, I would like to know if there is a cleaner way of testing the significance of $a$ and $\phi$ - and how the corresponding standard errors are calculated. Thanks in advance for your help!