categorizing a variable turns it from insignificant to significant The Next CEO of Stack OverflowVariable entered in logistic regression model is part of another variable entered in the same modelHow to modify variables to be significant in logistic regression?Why does adding independent variables make all independent variables insignificant?Can a variable become statistically significant after the addition of another variable?Can a previously insignificant variable become significant in forward stepwise regressionSignificance of variable but low impact on log likelihood?Categorizing Continuous Random Variable in Logistic RegressionHow can a predictor be significant, only on the presence of non-significant ones?Variable changes from not significant to significant, don't know why, please helpLinear Regression in groups / Multivariate regression
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categorizing a variable turns it from insignificant to significant
The Next CEO of Stack OverflowVariable entered in logistic regression model is part of another variable entered in the same modelHow to modify variables to be significant in logistic regression?Why does adding independent variables make all independent variables insignificant?Can a variable become statistically significant after the addition of another variable?Can a previously insignificant variable become significant in forward stepwise regressionSignificance of variable but low impact on log likelihood?Categorizing Continuous Random Variable in Logistic RegressionHow can a predictor be significant, only on the presence of non-significant ones?Variable changes from not significant to significant, don't know why, please helpLinear Regression in groups / Multivariate regression
$begingroup$
I have a numeric variable which turns out not significant in a multivariate logistic regression model.
However, when I categorize it into groups, suddenly it becomes significant.
This is very counter-intuitive to me: when categorizing a variable, we give some information up.
How can this be?
regression logistic statistical-significance multivariate-analysis
edited Mar 19 at 9:53
kjetil b halvorsen
31.7k984234
asked Mar 19 at 5:58
Omry AtiaOmry Atia
31010
$endgroup$
add a comment |
$begingroup$
I have a numeric variable which turns out not significant in a multivariate logistic regression model.
However, when I categorize it into groups, suddenly it becomes significant.
This is very counter-intuitive to me: when categorizing a variable, we give some information up.
How can this be?
regression logistic statistical-significance multivariate-analysis
edited Mar 19 at 9:53
kjetil b halvorsen
31.7k984234
asked Mar 19 at 5:58
Omry AtiaOmry Atia
31010
$endgroup$
add a comment |
$begingroup$
I have a numeric variable which turns out not significant in a multivariate logistic regression model.
However, when I categorize it into groups, suddenly it becomes significant.
This is very counter-intuitive to me: when categorizing a variable, we give some information up.
How can this be?
regression logistic statistical-significance multivariate-analysis
edited Mar 19 at 9:53
kjetil b halvorsen
31.7k984234
asked Mar 19 at 5:58
Omry AtiaOmry Atia
31010
$endgroup$
I have a numeric variable which turns out not significant in a multivariate logistic regression model.
However, when I categorize it into groups, suddenly it becomes significant.
This is very counter-intuitive to me: when categorizing a variable, we give some information up.
How can this be?
regression logistic statistical-significance multivariate-analysis
regression logistic statistical-significance multivariate-analysis
edited Mar 19 at 9:53
kjetil b halvorsen
31.7k984234
asked Mar 19 at 5:58
Omry AtiaOmry Atia
31010
edited Mar 19 at 9:53
kjetil b halvorsen
31.7k984234
asked Mar 19 at 5:58
Omry AtiaOmry Atia
31010
edited Mar 19 at 9:53
kjetil b halvorsen
31.7k984234
edited Mar 19 at 9:53
kjetil b halvorsen
31.7k984234
edited Mar 19 at 9:53
kjetil b halvorsen
31.7k984234
31.7k984234
asked Mar 19 at 5:58
Omry AtiaOmry Atia
31010
asked Mar 19 at 5:58
Omry AtiaOmry Atia
31010
asked Mar 19 at 5:58
Omry AtiaOmry Atia
31010
31010
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
One possible explanation would be nonlinearities in the relationship between your outcome and the predictor.
Here is a little example. We use a predictor that is uniform on $[-1,1]$. The outcome, however, does not linearly depend on the predictor, but on the square of the predictor: TRUE is more likely for both $xapprox-1$ and $xapprox 1$, but less likely for $xapprox 0$. In this case, a linear model will come up insignificant, but cutting the predictor into intervals makes it significant.
> set.seed(1)
> nn <- 1e3
> xx <- runif(nn,-1,1)
> yy <- runif(nn)<1/(1+exp(-xx^2))
>
> library(lmtest)
>
> model_0 <- glm(yy~1,family="binomial")
> model_1 <- glm(yy~xx,family="binomial")
> lrtest(model_1,model_0)
Likelihood ratio test
Model 1: yy ~ xx
Model 2: yy ~ 1
#Df LogLik Df Chisq Pr(>Chisq)
1 2 -676.72
2 1 -677.22 -1 0.9914 0.3194
>
> xx_cut <- cut(xx,c(-1,-0.3,0.3,1))
> model_2 <- glm(yy~xx_cut,family="binomial")
> lrtest(model_2,model_0)
Likelihood ratio test
Model 1: yy ~ xx_cut
Model 2: yy ~ 1
#Df LogLik Df Chisq Pr(>Chisq)
1 3 -673.65
2 1 -677.22 -2 7.1362 0.02821 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
However, this does not mean that discretizing the predictor is the best approach. (It almost never is.) Much better to model the nonlinearity using splines or similar.
answered Mar 19 at 6:22
Stephan KolassaStephan Kolassa
47.2k7100175
$endgroup$
$begingroup$
Are there some examples where discretizing might be sensible? For example, if you have a specific threshold (e.g. age 18) at which a binary switch in outcomes occurs. Numeric age in the 18+ range might not be significant, but binary age >18 might be significant?
$endgroup$
– ajrwhite
Mar 19 at 18:40
3
$begingroup$
@ajrwhite: it depends on the field. Anywhere that thresholds are codified in law discretization might make sense. E.g., if you model voting behavior, it makes sense to check whether someone is actually eligible to vote at age 18. Similarly, in Germany, your vehicle tax depends on your engine displacement and jumps at 1700, 1800, 1900, ... ccm, so pretty much all cars have displacements of 1699, 1799, ... ccm (kind of self-discretizing). In the natural sciences like biology, medicine, psychology etc., I struggle to find an example where discretization makes sense.
$endgroup$
– Stephan Kolassa
Mar 20 at 6:03
add a comment |
$begingroup$
One possible way is if the relationship is distinctly nonlinear. It's not possible to tell (given the lack of detail) whether this really explains what's going on.
You can check for yourself. First, you could do an added variable plot for the variable as itself, and you could also plot the fitted effects in the factor-version of the model. If the explanation is right, both should see a distinctly nonlinear pattern.
answered Mar 19 at 6:23
Glen_b♦Glen_b
214k23417769
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
One possible explanation would be nonlinearities in the relationship between your outcome and the predictor.
Here is a little example. We use a predictor that is uniform on $[-1,1]$. The outcome, however, does not linearly depend on the predictor, but on the square of the predictor: TRUE is more likely for both $xapprox-1$ and $xapprox 1$, but less likely for $xapprox 0$. In this case, a linear model will come up insignificant, but cutting the predictor into intervals makes it significant.
> set.seed(1)
> nn <- 1e3
> xx <- runif(nn,-1,1)
> yy <- runif(nn)<1/(1+exp(-xx^2))
>
> library(lmtest)
>
> model_0 <- glm(yy~1,family="binomial")
> model_1 <- glm(yy~xx,family="binomial")
> lrtest(model_1,model_0)
Likelihood ratio test
Model 1: yy ~ xx
Model 2: yy ~ 1
#Df LogLik Df Chisq Pr(>Chisq)
1 2 -676.72
2 1 -677.22 -1 0.9914 0.3194
>
> xx_cut <- cut(xx,c(-1,-0.3,0.3,1))
> model_2 <- glm(yy~xx_cut,family="binomial")
> lrtest(model_2,model_0)
Likelihood ratio test
Model 1: yy ~ xx_cut
Model 2: yy ~ 1
#Df LogLik Df Chisq Pr(>Chisq)
1 3 -673.65
2 1 -677.22 -2 7.1362 0.02821 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
However, this does not mean that discretizing the predictor is the best approach. (It almost never is.) Much better to model the nonlinearity using splines or similar.
answered Mar 19 at 6:22
Stephan KolassaStephan Kolassa
47.2k7100175
$endgroup$
$begingroup$
Are there some examples where discretizing might be sensible? For example, if you have a specific threshold (e.g. age 18) at which a binary switch in outcomes occurs. Numeric age in the 18+ range might not be significant, but binary age >18 might be significant?
$endgroup$
– ajrwhite
Mar 19 at 18:40
3
$begingroup$
@ajrwhite: it depends on the field. Anywhere that thresholds are codified in law discretization might make sense. E.g., if you model voting behavior, it makes sense to check whether someone is actually eligible to vote at age 18. Similarly, in Germany, your vehicle tax depends on your engine displacement and jumps at 1700, 1800, 1900, ... ccm, so pretty much all cars have displacements of 1699, 1799, ... ccm (kind of self-discretizing). In the natural sciences like biology, medicine, psychology etc., I struggle to find an example where discretization makes sense.
$endgroup$
– Stephan Kolassa
Mar 20 at 6:03
add a comment |
$begingroup$
One possible explanation would be nonlinearities in the relationship between your outcome and the predictor.
Here is a little example. We use a predictor that is uniform on $[-1,1]$. The outcome, however, does not linearly depend on the predictor, but on the square of the predictor: TRUE is more likely for both $xapprox-1$ and $xapprox 1$, but less likely for $xapprox 0$. In this case, a linear model will come up insignificant, but cutting the predictor into intervals makes it significant.
> set.seed(1)
> nn <- 1e3
> xx <- runif(nn,-1,1)
> yy <- runif(nn)<1/(1+exp(-xx^2))
>
> library(lmtest)
>
> model_0 <- glm(yy~1,family="binomial")
> model_1 <- glm(yy~xx,family="binomial")
> lrtest(model_1,model_0)
Likelihood ratio test
Model 1: yy ~ xx
Model 2: yy ~ 1
#Df LogLik Df Chisq Pr(>Chisq)
1 2 -676.72
2 1 -677.22 -1 0.9914 0.3194
>
> xx_cut <- cut(xx,c(-1,-0.3,0.3,1))
> model_2 <- glm(yy~xx_cut,family="binomial")
> lrtest(model_2,model_0)
Likelihood ratio test
Model 1: yy ~ xx_cut
Model 2: yy ~ 1
#Df LogLik Df Chisq Pr(>Chisq)
1 3 -673.65
2 1 -677.22 -2 7.1362 0.02821 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
However, this does not mean that discretizing the predictor is the best approach. (It almost never is.) Much better to model the nonlinearity using splines or similar.
answered Mar 19 at 6:22
Stephan KolassaStephan Kolassa
47.2k7100175
$endgroup$
$begingroup$
Are there some examples where discretizing might be sensible? For example, if you have a specific threshold (e.g. age 18) at which a binary switch in outcomes occurs. Numeric age in the 18+ range might not be significant, but binary age >18 might be significant?
$endgroup$
– ajrwhite
Mar 19 at 18:40
3
$begingroup$
@ajrwhite: it depends on the field. Anywhere that thresholds are codified in law discretization might make sense. E.g., if you model voting behavior, it makes sense to check whether someone is actually eligible to vote at age 18. Similarly, in Germany, your vehicle tax depends on your engine displacement and jumps at 1700, 1800, 1900, ... ccm, so pretty much all cars have displacements of 1699, 1799, ... ccm (kind of self-discretizing). In the natural sciences like biology, medicine, psychology etc., I struggle to find an example where discretization makes sense.
$endgroup$
– Stephan Kolassa
Mar 20 at 6:03
add a comment |
$begingroup$
One possible explanation would be nonlinearities in the relationship between your outcome and the predictor.
Here is a little example. We use a predictor that is uniform on $[-1,1]$. The outcome, however, does not linearly depend on the predictor, but on the square of the predictor: TRUE is more likely for both $xapprox-1$ and $xapprox 1$, but less likely for $xapprox 0$. In this case, a linear model will come up insignificant, but cutting the predictor into intervals makes it significant.
> set.seed(1)
> nn <- 1e3
> xx <- runif(nn,-1,1)
> yy <- runif(nn)<1/(1+exp(-xx^2))
>
> library(lmtest)
>
> model_0 <- glm(yy~1,family="binomial")
> model_1 <- glm(yy~xx,family="binomial")
> lrtest(model_1,model_0)
Likelihood ratio test
Model 1: yy ~ xx
Model 2: yy ~ 1
#Df LogLik Df Chisq Pr(>Chisq)
1 2 -676.72
2 1 -677.22 -1 0.9914 0.3194
>
> xx_cut <- cut(xx,c(-1,-0.3,0.3,1))
> model_2 <- glm(yy~xx_cut,family="binomial")
> lrtest(model_2,model_0)
Likelihood ratio test
Model 1: yy ~ xx_cut
Model 2: yy ~ 1
#Df LogLik Df Chisq Pr(>Chisq)
1 3 -673.65
2 1 -677.22 -2 7.1362 0.02821 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
However, this does not mean that discretizing the predictor is the best approach. (It almost never is.) Much better to model the nonlinearity using splines or similar.
answered Mar 19 at 6:22
Stephan KolassaStephan Kolassa
47.2k7100175
$endgroup$
One possible explanation would be nonlinearities in the relationship between your outcome and the predictor.
Here is a little example. We use a predictor that is uniform on $[-1,1]$. The outcome, however, does not linearly depend on the predictor, but on the square of the predictor: TRUE is more likely for both $xapprox-1$ and $xapprox 1$, but less likely for $xapprox 0$. In this case, a linear model will come up insignificant, but cutting the predictor into intervals makes it significant.
> set.seed(1)
> nn <- 1e3
> xx <- runif(nn,-1,1)
> yy <- runif(nn)<1/(1+exp(-xx^2))
>
> library(lmtest)
>
> model_0 <- glm(yy~1,family="binomial")
> model_1 <- glm(yy~xx,family="binomial")
> lrtest(model_1,model_0)
Likelihood ratio test
Model 1: yy ~ xx
Model 2: yy ~ 1
#Df LogLik Df Chisq Pr(>Chisq)
1 2 -676.72
2 1 -677.22 -1 0.9914 0.3194
>
> xx_cut <- cut(xx,c(-1,-0.3,0.3,1))
> model_2 <- glm(yy~xx_cut,family="binomial")
> lrtest(model_2,model_0)
Likelihood ratio test
Model 1: yy ~ xx_cut
Model 2: yy ~ 1
#Df LogLik Df Chisq Pr(>Chisq)
1 3 -673.65
2 1 -677.22 -2 7.1362 0.02821 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
However, this does not mean that discretizing the predictor is the best approach. (It almost never is.) Much better to model the nonlinearity using splines or similar.
answered Mar 19 at 6:22
Stephan KolassaStephan Kolassa
47.2k7100175
answered Mar 19 at 6:22
Stephan KolassaStephan Kolassa
47.2k7100175
answered Mar 19 at 6:22
Stephan KolassaStephan Kolassa
47.2k7100175
answered Mar 19 at 6:22
Stephan KolassaStephan Kolassa
47.2k7100175
47.2k7100175
$begingroup$
Are there some examples where discretizing might be sensible? For example, if you have a specific threshold (e.g. age 18) at which a binary switch in outcomes occurs. Numeric age in the 18+ range might not be significant, but binary age >18 might be significant?
$endgroup$
– ajrwhite
Mar 19 at 18:40
3
$begingroup$
@ajrwhite: it depends on the field. Anywhere that thresholds are codified in law discretization might make sense. E.g., if you model voting behavior, it makes sense to check whether someone is actually eligible to vote at age 18. Similarly, in Germany, your vehicle tax depends on your engine displacement and jumps at 1700, 1800, 1900, ... ccm, so pretty much all cars have displacements of 1699, 1799, ... ccm (kind of self-discretizing). In the natural sciences like biology, medicine, psychology etc., I struggle to find an example where discretization makes sense.
$endgroup$
– Stephan Kolassa
Mar 20 at 6:03
add a comment |
$begingroup$
Are there some examples where discretizing might be sensible? For example, if you have a specific threshold (e.g. age 18) at which a binary switch in outcomes occurs. Numeric age in the 18+ range might not be significant, but binary age >18 might be significant?
$endgroup$
– ajrwhite
Mar 19 at 18:40
3
$begingroup$
@ajrwhite: it depends on the field. Anywhere that thresholds are codified in law discretization might make sense. E.g., if you model voting behavior, it makes sense to check whether someone is actually eligible to vote at age 18. Similarly, in Germany, your vehicle tax depends on your engine displacement and jumps at 1700, 1800, 1900, ... ccm, so pretty much all cars have displacements of 1699, 1799, ... ccm (kind of self-discretizing). In the natural sciences like biology, medicine, psychology etc., I struggle to find an example where discretization makes sense.
$endgroup$
– Stephan Kolassa
Mar 20 at 6:03
$begingroup$
Are there some examples where discretizing might be sensible? For example, if you have a specific threshold (e.g. age 18) at which a binary switch in outcomes occurs. Numeric age in the 18+ range might not be significant, but binary age >18 might be significant?
$endgroup$
– ajrwhite
Mar 19 at 18:40
$begingroup$
Are there some examples where discretizing might be sensible? For example, if you have a specific threshold (e.g. age 18) at which a binary switch in outcomes occurs. Numeric age in the 18+ range might not be significant, but binary age >18 might be significant?
$endgroup$
– ajrwhite
Mar 19 at 18:40
3
3
$begingroup$
@ajrwhite: it depends on the field. Anywhere that thresholds are codified in law discretization might make sense. E.g., if you model voting behavior, it makes sense to check whether someone is actually eligible to vote at age 18. Similarly, in Germany, your vehicle tax depends on your engine displacement and jumps at 1700, 1800, 1900, ... ccm, so pretty much all cars have displacements of 1699, 1799, ... ccm (kind of self-discretizing). In the natural sciences like biology, medicine, psychology etc., I struggle to find an example where discretization makes sense.
$endgroup$
– Stephan Kolassa
Mar 20 at 6:03
$begingroup$
@ajrwhite: it depends on the field. Anywhere that thresholds are codified in law discretization might make sense. E.g., if you model voting behavior, it makes sense to check whether someone is actually eligible to vote at age 18. Similarly, in Germany, your vehicle tax depends on your engine displacement and jumps at 1700, 1800, 1900, ... ccm, so pretty much all cars have displacements of 1699, 1799, ... ccm (kind of self-discretizing). In the natural sciences like biology, medicine, psychology etc., I struggle to find an example where discretization makes sense.
$endgroup$
– Stephan Kolassa
Mar 20 at 6:03
add a comment |
$begingroup$
One possible way is if the relationship is distinctly nonlinear. It's not possible to tell (given the lack of detail) whether this really explains what's going on.
You can check for yourself. First, you could do an added variable plot for the variable as itself, and you could also plot the fitted effects in the factor-version of the model. If the explanation is right, both should see a distinctly nonlinear pattern.
answered Mar 19 at 6:23
Glen_b♦Glen_b
214k23417769
$endgroup$
add a comment |
$begingroup$
One possible way is if the relationship is distinctly nonlinear. It's not possible to tell (given the lack of detail) whether this really explains what's going on.
You can check for yourself. First, you could do an added variable plot for the variable as itself, and you could also plot the fitted effects in the factor-version of the model. If the explanation is right, both should see a distinctly nonlinear pattern.
answered Mar 19 at 6:23
Glen_b♦Glen_b
214k23417769
$endgroup$
add a comment |
$begingroup$
One possible way is if the relationship is distinctly nonlinear. It's not possible to tell (given the lack of detail) whether this really explains what's going on.
You can check for yourself. First, you could do an added variable plot for the variable as itself, and you could also plot the fitted effects in the factor-version of the model. If the explanation is right, both should see a distinctly nonlinear pattern.
answered Mar 19 at 6:23
Glen_b♦Glen_b
214k23417769
$endgroup$
One possible way is if the relationship is distinctly nonlinear. It's not possible to tell (given the lack of detail) whether this really explains what's going on.
You can check for yourself. First, you could do an added variable plot for the variable as itself, and you could also plot the fitted effects in the factor-version of the model. If the explanation is right, both should see a distinctly nonlinear pattern.
answered Mar 19 at 6:23
Glen_b♦Glen_b
214k23417769
edited Mar 19 at 14:58
answered Mar 19 at 6:23
Glen_b♦Glen_b
214k23417769
answered Mar 19 at 6:23
Glen_b♦Glen_b
214k23417769
answered Mar 19 at 6:23
Glen_b♦Glen_b
214k23417769
214k23417769
add a comment |
add a comment |
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Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
