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categorizing a variable turns it from insignificant to significant

Variable 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

17

$begingroup$

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

share|cite|improve this question

edited Mar 19 at 9:53

kjetil b halvorsen

31.3k984224

asked Mar 19 at 5:58

Omry AtiaOmry Atia

30510

$endgroup$

add a comment | 

17

$begingroup$

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

share|cite|improve this question

edited Mar 19 at 9:53

kjetil b halvorsen

31.3k984224

asked Mar 19 at 5:58

Omry AtiaOmry Atia

30510

$endgroup$

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

share|cite|improve this question

edited Mar 19 at 9:53

kjetil b halvorsen

31.3k984224

asked Mar 19 at 5:58

Omry AtiaOmry Atia

30510

$endgroup$

share|cite|improve this question

edited Mar 19 at 9:53

kjetil b halvorsen

31.3k984224

asked Mar 19 at 5:58

Omry AtiaOmry Atia

30510

share|cite|improve this question

edited Mar 19 at 9:53

kjetil b halvorsen

31.3k984224

asked Mar 19 at 5:58

Omry AtiaOmry Atia

30510

edited Mar 19 at 9:53

kjetil b halvorsen

31.3k984224

edited Mar 19 at 9:53

kjetil b halvorsen

31.3k984224

asked Mar 19 at 5:58

Omry AtiaOmry Atia

30510

asked Mar 19 at 5:58

Omry AtiaOmry Atia

30510

2 Answers
2

active

oldest

votes

25

$begingroup$

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.

share|cite|improve this answer

answered Mar 19 at 6:22

Stephan KolassaStephan Kolassa

47k7100175

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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 | 

7

$begingroup$

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.

share|cite|improve this answer

edited Mar 19 at 14:58

answered Mar 19 at 6:23

Glen_b♦Glen_b

214k23415765

$endgroup$

add a comment | 

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25

$begingroup$

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.

share|cite|improve this answer

answered Mar 19 at 6:22

Stephan KolassaStephan Kolassa

47k7100175

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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 | 

25

$begingroup$

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.

share|cite|improve this answer

answered Mar 19 at 6:22

Stephan KolassaStephan Kolassa

47k7100175

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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.

share|cite|improve this answer

answered Mar 19 at 6:22

Stephan KolassaStephan Kolassa

47k7100175

$endgroup$

> 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

share|cite|improve this answer

answered Mar 19 at 6:22

Stephan KolassaStephan Kolassa

47k7100175

answered Mar 19 at 6:22

Stephan KolassaStephan Kolassa

47k7100175

answered Mar 19 at 6:22

Stephan KolassaStephan Kolassa

47k7100175

7

$begingroup$

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.

share|cite|improve this answer

edited Mar 19 at 14:58

answered Mar 19 at 6:23

Glen_b♦Glen_b

214k23415765

$endgroup$

add a comment | 

7

$begingroup$

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.

share|cite|improve this answer

edited Mar 19 at 14:58

answered Mar 19 at 6:23

Glen_b♦Glen_b

214k23415765

$endgroup$

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.

share|cite|improve this answer

edited Mar 19 at 14:58

answered Mar 19 at 6:23

Glen_b♦Glen_b

214k23415765

$endgroup$

share|cite|improve this answer

edited Mar 19 at 14:58

answered Mar 19 at 6:23

Glen_b♦Glen_b

214k23415765

answered Mar 19 at 6:23

Glen_b♦Glen_b

214k23415765

answered Mar 19 at 6:23

Glen_b♦Glen_b

214k23415765