PCA for index construction. Problem with a sign
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I am using R (RStudio) to construct an index/synthetic indicator to evaluate, say, commercial efficiency. I am using the PCA() command from factorMineR package, and using 7 distinct variables. I have previously created similar indexes by calculating the weight of each particular variable over the first component (which can be obtained through PCA()$var$coord[,1]), with no problems, since each variable has a positive weight. However, there is one particular variable that has a weight with an undesired sign: negative. The variable is ‘delivery speed’ and this sign would imply that the greater the speed the less efficient the process. Then, what is going on? How would you amend this issue, preferably still using PCA?
r rstudio pca
asked Nov 22 '18 at 19:50
LALO365LALO365
1
add a comment |
I am using R (RStudio) to construct an index/synthetic indicator to evaluate, say, commercial efficiency. I am using the PCA() command from factorMineR package, and using 7 distinct variables. I have previously created similar indexes by calculating the weight of each particular variable over the first component (which can be obtained through PCA()$var$coord[,1]), with no problems, since each variable has a positive weight. However, there is one particular variable that has a weight with an undesired sign: negative. The variable is ‘delivery speed’ and this sign would imply that the greater the speed the less efficient the process. Then, what is going on? How would you amend this issue, preferably still using PCA?
r rstudio pca
asked Nov 22 '18 at 19:50
LALO365LALO365
1
A reproducible example code would greatly improve the changes to get an answer.
– Heikki
Nov 22 '18 at 20:10
add a comment |
I am using R (RStudio) to construct an index/synthetic indicator to evaluate, say, commercial efficiency. I am using the PCA() command from factorMineR package, and using 7 distinct variables. I have previously created similar indexes by calculating the weight of each particular variable over the first component (which can be obtained through PCA()$var$coord[,1]), with no problems, since each variable has a positive weight. However, there is one particular variable that has a weight with an undesired sign: negative. The variable is ‘delivery speed’ and this sign would imply that the greater the speed the less efficient the process. Then, what is going on? How would you amend this issue, preferably still using PCA?
r rstudio pca
asked Nov 22 '18 at 19:50
LALO365LALO365
1
I am using R (RStudio) to construct an index/synthetic indicator to evaluate, say, commercial efficiency. I am using the PCA() command from factorMineR package, and using 7 distinct variables. I have previously created similar indexes by calculating the weight of each particular variable over the first component (which can be obtained through PCA()$var$coord[,1]), with no problems, since each variable has a positive weight. However, there is one particular variable that has a weight with an undesired sign: negative. The variable is ‘delivery speed’ and this sign would imply that the greater the speed the less efficient the process. Then, what is going on? How would you amend this issue, preferably still using PCA?
r rstudio pca
r rstudio pca
asked Nov 22 '18 at 19:50
LALO365LALO365
1
asked Nov 22 '18 at 19:50
LALO365LALO365
1
asked Nov 22 '18 at 19:50
LALO365LALO365
1
asked Nov 22 '18 at 19:50
LALO365LALO365
1
asked Nov 22 '18 at 19:50
LALO365LALO365
1
1
A reproducible example code would greatly improve the changes to get an answer.
– Heikki
Nov 22 '18 at 20:10
add a comment |
A reproducible example code would greatly improve the changes to get an answer.
– Heikki
Nov 22 '18 at 20:10
A reproducible example code would greatly improve the changes to get an answer.
– Heikki
Nov 22 '18 at 20:10
A reproducible example code would greatly improve the changes to get an answer.
– Heikki
Nov 22 '18 at 20:10
add a comment |
1 Answer
1
active
oldest
votes
The sign of variable weights shouldn't matter in PCA. Since on the whole, all of the components perfectly represent the original data (when p < n), for some components it is natural that there will be some positive weights and some negative weights. That doesn't mean that that particular variable has an undesired weight, rather that for that particular extracted signal (say, first principal component) the variable weight is negative.
For a better understanding, let's take the classical 2 dimensional example, which I took from this very useful discussion:
Can you see from the graph that one of the weights will necessary be negative for the 2nd principal component?
Finally, if that variable does actually disturb your analysis, one possible solution would be to apply Sparse PCA. Under cross-validated regularization that method is able to make some of the weights equal to zero. If in your case that negative weight is not significant enough, it might get reduced to zero under SPCA.
answered Nov 22 '18 at 20:31
NutleNutle
318217
I understand the geometric implications of PCA, it is just that I found that sign curious since PCA didn’t previously surprise me with an unexpected sign and actually it is frequently used for index construction. I agree that negative signs derived from PCA are not casual. However, given this personal inconvenient could you suggest me a better procedure (even if it is not PCA) for index construction given a set of variables? I’m currently trying to assign a small weight to this variable with respect to other ones and mantain fixed the other variables' weights
– LALO365
Nov 22 '18 at 21:46
add a comment |
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The sign of variable weights shouldn't matter in PCA. Since on the whole, all of the components perfectly represent the original data (when p < n), for some components it is natural that there will be some positive weights and some negative weights. That doesn't mean that that particular variable has an undesired weight, rather that for that particular extracted signal (say, first principal component) the variable weight is negative.
For a better understanding, let's take the classical 2 dimensional example, which I took from this very useful discussion:
Can you see from the graph that one of the weights will necessary be negative for the 2nd principal component?
Finally, if that variable does actually disturb your analysis, one possible solution would be to apply Sparse PCA. Under cross-validated regularization that method is able to make some of the weights equal to zero. If in your case that negative weight is not significant enough, it might get reduced to zero under SPCA.
answered Nov 22 '18 at 20:31
NutleNutle
318217
I understand the geometric implications of PCA, it is just that I found that sign curious since PCA didn’t previously surprise me with an unexpected sign and actually it is frequently used for index construction. I agree that negative signs derived from PCA are not casual. However, given this personal inconvenient could you suggest me a better procedure (even if it is not PCA) for index construction given a set of variables? I’m currently trying to assign a small weight to this variable with respect to other ones and mantain fixed the other variables' weights
– LALO365
Nov 22 '18 at 21:46
add a comment |
The sign of variable weights shouldn't matter in PCA. Since on the whole, all of the components perfectly represent the original data (when p < n), for some components it is natural that there will be some positive weights and some negative weights. That doesn't mean that that particular variable has an undesired weight, rather that for that particular extracted signal (say, first principal component) the variable weight is negative.
For a better understanding, let's take the classical 2 dimensional example, which I took from this very useful discussion:
Can you see from the graph that one of the weights will necessary be negative for the 2nd principal component?
Finally, if that variable does actually disturb your analysis, one possible solution would be to apply Sparse PCA. Under cross-validated regularization that method is able to make some of the weights equal to zero. If in your case that negative weight is not significant enough, it might get reduced to zero under SPCA.
answered Nov 22 '18 at 20:31
NutleNutle
318217
I understand the geometric implications of PCA, it is just that I found that sign curious since PCA didn’t previously surprise me with an unexpected sign and actually it is frequently used for index construction. I agree that negative signs derived from PCA are not casual. However, given this personal inconvenient could you suggest me a better procedure (even if it is not PCA) for index construction given a set of variables? I’m currently trying to assign a small weight to this variable with respect to other ones and mantain fixed the other variables' weights
– LALO365
Nov 22 '18 at 21:46
add a comment |
The sign of variable weights shouldn't matter in PCA. Since on the whole, all of the components perfectly represent the original data (when p < n), for some components it is natural that there will be some positive weights and some negative weights. That doesn't mean that that particular variable has an undesired weight, rather that for that particular extracted signal (say, first principal component) the variable weight is negative.
For a better understanding, let's take the classical 2 dimensional example, which I took from this very useful discussion:
Can you see from the graph that one of the weights will necessary be negative for the 2nd principal component?
Finally, if that variable does actually disturb your analysis, one possible solution would be to apply Sparse PCA. Under cross-validated regularization that method is able to make some of the weights equal to zero. If in your case that negative weight is not significant enough, it might get reduced to zero under SPCA.
answered Nov 22 '18 at 20:31
NutleNutle
318217
The sign of variable weights shouldn't matter in PCA. Since on the whole, all of the components perfectly represent the original data (when p < n), for some components it is natural that there will be some positive weights and some negative weights. That doesn't mean that that particular variable has an undesired weight, rather that for that particular extracted signal (say, first principal component) the variable weight is negative.
For a better understanding, let's take the classical 2 dimensional example, which I took from this very useful discussion:
Can you see from the graph that one of the weights will necessary be negative for the 2nd principal component?
Finally, if that variable does actually disturb your analysis, one possible solution would be to apply Sparse PCA. Under cross-validated regularization that method is able to make some of the weights equal to zero. If in your case that negative weight is not significant enough, it might get reduced to zero under SPCA.
answered Nov 22 '18 at 20:31
NutleNutle
318217
answered Nov 22 '18 at 20:31
NutleNutle
318217
answered Nov 22 '18 at 20:31
NutleNutle
318217
answered Nov 22 '18 at 20:31
NutleNutle
318217
318217
I understand the geometric implications of PCA, it is just that I found that sign curious since PCA didn’t previously surprise me with an unexpected sign and actually it is frequently used for index construction. I agree that negative signs derived from PCA are not casual. However, given this personal inconvenient could you suggest me a better procedure (even if it is not PCA) for index construction given a set of variables? I’m currently trying to assign a small weight to this variable with respect to other ones and mantain fixed the other variables' weights
– LALO365
Nov 22 '18 at 21:46
add a comment |
I understand the geometric implications of PCA, it is just that I found that sign curious since PCA didn’t previously surprise me with an unexpected sign and actually it is frequently used for index construction. I agree that negative signs derived from PCA are not casual. However, given this personal inconvenient could you suggest me a better procedure (even if it is not PCA) for index construction given a set of variables? I’m currently trying to assign a small weight to this variable with respect to other ones and mantain fixed the other variables' weights
– LALO365
Nov 22 '18 at 21:46
I understand the geometric implications of PCA, it is just that I found that sign curious since PCA didn’t previously surprise me with an unexpected sign and actually it is frequently used for index construction. I agree that negative signs derived from PCA are not casual. However, given this personal inconvenient could you suggest me a better procedure (even if it is not PCA) for index construction given a set of variables? I’m currently trying to assign a small weight to this variable with respect to other ones and mantain fixed the other variables' weights
– LALO365
Nov 22 '18 at 21:46
I understand the geometric implications of PCA, it is just that I found that sign curious since PCA didn’t previously surprise me with an unexpected sign and actually it is frequently used for index construction. I agree that negative signs derived from PCA are not casual. However, given this personal inconvenient could you suggest me a better procedure (even if it is not PCA) for index construction given a set of variables? I’m currently trying to assign a small weight to this variable with respect to other ones and mantain fixed the other variables' weights
– LALO365
Nov 22 '18 at 21:46
add a comment |
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A reproducible example code would greatly improve the changes to get an answer.
– Heikki
Nov 22 '18 at 20:10