I have a question regarding the Johnson transformation in Minitab. If applied to separate predictor variables, can the R-squared output of separate linear regression using each of these variables be compared, even though the Johnson transformation will use a slightly different equation to being each to a normal distribution?
My intention was to compare R-squared values of single predictors in linear regressions, following the practice of Dr. Stuart Wagenius in his 'Scale dependence of reproductive failure in fragmented Echinacea populations. Ecology 87:931-941'
Reg
Flower life = B0 + B1 (number of flowers at 1 meter radius i.e. density) + Ei
Flower life = B0 + B1 (number of flowers at 5 meter radius i.e. density) + Ei
Flower life = B0 + B1 (number of flowers at 10 meter radius i.e. density) + Ei
and even
Reg
Flower life = B0 + B1 (distance to 1st nearest flowering neighbor i.e. isolation) + Ei
Flower life = B0 + B1 (distance to 2nd nearest flowering neighbor i.e. islolation) + Ei
Flower life = B0 + B1 (distance to 3rd nearest flowering neighbor i.e. isolation) + Ei
The intention is to find out which spatial scales are most correlated with the response variable flower life, and which means of measuring "floral neighborhood" (density or isolation) is better at predicting how long a flower lives. These two predictors are highly correlated ans thus cannot be placed in the same model. Imagine 100 random plants for which I have collected this data(flower life, number of neighbors at each radius 1, 5, 10 and the distance to 1st, 2nd, and 3rd nearest neighbor). Consider the situation and models as simple as possible: except that I have found the best transformation for both the predictor variables (Density and Isolation) is the Johnson Transformation (in Minitab). Then for each predictor variable a separate (slightly different) "transformation function" is applied.
Can I still compare R-squared values between the models? The response variable dataset is the same in each model, the chosen type of transformation (Johnson) is the same for all predictor variables, only the predicting variable is different in each model (1 m density, 5 m density, 10 m density, 1st nnd, 2nd nnd, 3rd nnd).
Thanks for your time and effort in reading this email and making any comments, suggestions, or offering any leads whatsoever,
Here is the paper which I referred to: http://echinacea.umn.edu/pdf/wagenius2006.pdf
My intention was to compare R-squared values of single predictors in linear regressions, following the practice of Dr. Stuart Wagenius in his 'Scale dependence of reproductive failure in fragmented Echinacea populations. Ecology 87:931-941'
Reg
Flower life = B0 + B1 (number of flowers at 1 meter radius i.e. density) + Ei
Flower life = B0 + B1 (number of flowers at 5 meter radius i.e. density) + Ei
Flower life = B0 + B1 (number of flowers at 10 meter radius i.e. density) + Ei
and even
Reg
Flower life = B0 + B1 (distance to 1st nearest flowering neighbor i.e. isolation) + Ei
Flower life = B0 + B1 (distance to 2nd nearest flowering neighbor i.e. islolation) + Ei
Flower life = B0 + B1 (distance to 3rd nearest flowering neighbor i.e. isolation) + Ei
The intention is to find out which spatial scales are most correlated with the response variable flower life, and which means of measuring "floral neighborhood" (density or isolation) is better at predicting how long a flower lives. These two predictors are highly correlated ans thus cannot be placed in the same model. Imagine 100 random plants for which I have collected this data(flower life, number of neighbors at each radius 1, 5, 10 and the distance to 1st, 2nd, and 3rd nearest neighbor). Consider the situation and models as simple as possible: except that I have found the best transformation for both the predictor variables (Density and Isolation) is the Johnson Transformation (in Minitab). Then for each predictor variable a separate (slightly different) "transformation function" is applied.
Can I still compare R-squared values between the models? The response variable dataset is the same in each model, the chosen type of transformation (Johnson) is the same for all predictor variables, only the predicting variable is different in each model (1 m density, 5 m density, 10 m density, 1st nnd, 2nd nnd, 3rd nnd).
Thanks for your time and effort in reading this email and making any comments, suggestions, or offering any leads whatsoever,
Here is the paper which I referred to: http://echinacea.umn.edu/pdf/wagenius2006.pdf