How does quantile regression compare to logistic regression with the variable split at the quantile?Analyzing...
Why "Having chlorophyll without photosynthesis is actually very dangerous" and "like living with a bomb"?
When a company launches a new product do they "come out" with a new product or do they "come up" with a new product?
Arrow those variables!
How much of data wrangling is a data scientist's job?
Why are electrically insulating heatsinks so rare? Is it just cost?
Why do I get two different answers for this counting problem?
What does the "remote control" for a QF-4 look like?
Why is consensus so controversial in Britain?
dbcc cleantable batch size explanation
Find the result of this dual key cipher
What would happen to a modern skyscraper if it rains micro blackholes?
Can I make popcorn with any corn?
If human space travel is limited by the G force vulnerability, is there a way to counter G forces?
Accidentally leaked the solution to an assignment, what to do now? (I'm the prof)
Why is Minecraft giving an OpenGL error?
How can bays and straits be determined in a procedurally generated map?
How can I prevent hyper evolved versions of regular creatures from wiping out their cousins?
What typically incentivizes a professor to change jobs to a lower ranking university?
Can a Cauchy sequence converge for one metric while not converging for another?
How do I deal with an unproductive colleague in a small company?
Why can't we play rap on piano?
Languages that we cannot (dis)prove to be Context-Free
Why doesn't H₄O²⁺ exist?
Why can't I see bouncing of a switch on an oscilloscope?
How does quantile regression compare to logistic regression with the variable split at the quantile?
Analyzing Logistic Regression when not using a dichotomous dependent variableEstimating logistic regression coefficients in a case-control design when the outcome variable is not case/control statusWhen does quantile regression produce biased coefficients (if ever)?How can I account for a nonlinear variable in a logistic regression?Variable Selection for Logistic regressionlogistic regression: the relation between sample proportion and prediction?How to compare the performance of two classification methods? (logistic regression and classification trees)Unbalanced Design with a Large Data Set and Logistic RegressionFit logistic regression with linear constraints on coefficients in RLogistic regression with double censored independent variable
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ margin-bottom:0;
}
$begingroup$
I googled a bit but didn't find anything on this.
Suppose you do a quantile regression on the qth quantile of the dependent variable.
Then you split the DV at the qth quantile and label the result 0 and 1. Then you do logistic regression on the categorized DV.
I'm looking for any Monte-Carlo studies of this or reasons to prefer one over the other etc.
logistic quantile-regression
$endgroup$
add a comment |
$begingroup$
I googled a bit but didn't find anything on this.
Suppose you do a quantile regression on the qth quantile of the dependent variable.
Then you split the DV at the qth quantile and label the result 0 and 1. Then you do logistic regression on the categorized DV.
I'm looking for any Monte-Carlo studies of this or reasons to prefer one over the other etc.
logistic quantile-regression
$endgroup$
1
$begingroup$
Could you show us any reasonable way even to compare the results of the two regressions? After all, unless you have something a little less general in mind, the coefficients of the regressors in these two models have entirely different meanings and interpretations, so in what sense are we to understand what you mean by "prefer"?
$endgroup$
– whuber♦
8 hours ago
add a comment |
$begingroup$
I googled a bit but didn't find anything on this.
Suppose you do a quantile regression on the qth quantile of the dependent variable.
Then you split the DV at the qth quantile and label the result 0 and 1. Then you do logistic regression on the categorized DV.
I'm looking for any Monte-Carlo studies of this or reasons to prefer one over the other etc.
logistic quantile-regression
$endgroup$
I googled a bit but didn't find anything on this.
Suppose you do a quantile regression on the qth quantile of the dependent variable.
Then you split the DV at the qth quantile and label the result 0 and 1. Then you do logistic regression on the categorized DV.
I'm looking for any Monte-Carlo studies of this or reasons to prefer one over the other etc.
logistic quantile-regression
logistic quantile-regression
asked 10 hours ago
Peter Flom♦Peter Flom
77k12109215
77k12109215
1
$begingroup$
Could you show us any reasonable way even to compare the results of the two regressions? After all, unless you have something a little less general in mind, the coefficients of the regressors in these two models have entirely different meanings and interpretations, so in what sense are we to understand what you mean by "prefer"?
$endgroup$
– whuber♦
8 hours ago
add a comment |
1
$begingroup$
Could you show us any reasonable way even to compare the results of the two regressions? After all, unless you have something a little less general in mind, the coefficients of the regressors in these two models have entirely different meanings and interpretations, so in what sense are we to understand what you mean by "prefer"?
$endgroup$
– whuber♦
8 hours ago
1
1
$begingroup$
Could you show us any reasonable way even to compare the results of the two regressions? After all, unless you have something a little less general in mind, the coefficients of the regressors in these two models have entirely different meanings and interpretations, so in what sense are we to understand what you mean by "prefer"?
$endgroup$
– whuber♦
8 hours ago
$begingroup$
Could you show us any reasonable way even to compare the results of the two regressions? After all, unless you have something a little less general in mind, the coefficients of the regressors in these two models have entirely different meanings and interpretations, so in what sense are we to understand what you mean by "prefer"?
$endgroup$
– whuber♦
8 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
For simplicity, assume you have a continuous dependent variable Y and a continuous predictor variable X.
Logistic Regression
If I understand your post correctly, your logistic regression will categorize Y into 0 and 1 based on the quantile of the (unconditional) distribution of Y. Specifically, the q-th quantile of the distribution of observed Y values will be computed and Ycat will be defined as 0 if Y is strictly less than this quantile and 1 if Y is greater than or equal to this quantile.
If the above captures your intent, then the logistic regression will model the odds of Y exceeding or being equal to the (observed) q-th quantile of the (unconditional) Y distribution as a function of X.
** Quantile Regression**
On the other hand, if you are performing a quantile regression of Y on X, you are focusing on modelling how the q-th quantile of the conditional distribution of Y given X changes as a function of X.
Logistic Regression versus Quantile Regression
It seems to me that these two procedures have totally different aims, since the first procedure (i.e., logistic regression) focuses on the q-th quantile of the unconditional distribution of Y, whereas the second procedure (i.e., quantile regression) focuses on the the q-th quantile of the conditional distribution of Y.
The unconditional distribution of Y is the
distribution of Y values (hence it ignores any
information about the X values).
The conditional distribution of Y given X is the
distribution of those Y values for which the values
of X are the same.
Illustrative Example
For illustration purposes, let's say Y = cholesterol and X = body weight.
Then logistic regression is modelling the odds of having a 'high' cholesterol value (i.e., greater than or equal to the q-th quantile of the observed cholesterol values) as a function of body weight, where the definition of 'high' has no relation to body weight. In other words, the marker for what constitutes a 'high' cholesterol value is independent of body weight. What changes with body weight in this model is the odds that a cholesterol value would exceed this marker.
On the other hand, quantile regression is looking at how the 'marker' cholesterol values for which q% of the subjects with the same body weight in the underlying population have a higher cholesterol value vary as a function of body weight. You can think of these cholesterol values as markers for identifying what cholesterol values are 'high' - but in this case, each marker depends on the corresponding body weight; furthermore, the markers are assumed to change in a predictable fashion as the value of X changes (e.g., the markers tend to increase as X increases).
$endgroup$
1
$begingroup$
I agree with all that. Yet, there does seem to be a similarity - that is, both look at the qth quantile as a function of the same independent variables.
$endgroup$
– Peter Flom♦
8 hours ago
2
$begingroup$
Yes, but the difference is that one method looks at the unconditional quantile (i.e., logistic regression) while the other looks at the conditional quantile (i.e., quantile regression). Those two quantiles keep track of different things.
$endgroup$
– Isabella Ghement
8 hours ago
add a comment |
$begingroup$
They won't be equal, and the reason is simple.
With quantile regression you want to model the quantile conditional of the independent variables. Your approach with logistic regression fits the marginal quantile.
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "65"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f401421%2fhow-does-quantile-regression-compare-to-logistic-regression-with-the-variable-sp%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
For simplicity, assume you have a continuous dependent variable Y and a continuous predictor variable X.
Logistic Regression
If I understand your post correctly, your logistic regression will categorize Y into 0 and 1 based on the quantile of the (unconditional) distribution of Y. Specifically, the q-th quantile of the distribution of observed Y values will be computed and Ycat will be defined as 0 if Y is strictly less than this quantile and 1 if Y is greater than or equal to this quantile.
If the above captures your intent, then the logistic regression will model the odds of Y exceeding or being equal to the (observed) q-th quantile of the (unconditional) Y distribution as a function of X.
** Quantile Regression**
On the other hand, if you are performing a quantile regression of Y on X, you are focusing on modelling how the q-th quantile of the conditional distribution of Y given X changes as a function of X.
Logistic Regression versus Quantile Regression
It seems to me that these two procedures have totally different aims, since the first procedure (i.e., logistic regression) focuses on the q-th quantile of the unconditional distribution of Y, whereas the second procedure (i.e., quantile regression) focuses on the the q-th quantile of the conditional distribution of Y.
The unconditional distribution of Y is the
distribution of Y values (hence it ignores any
information about the X values).
The conditional distribution of Y given X is the
distribution of those Y values for which the values
of X are the same.
Illustrative Example
For illustration purposes, let's say Y = cholesterol and X = body weight.
Then logistic regression is modelling the odds of having a 'high' cholesterol value (i.e., greater than or equal to the q-th quantile of the observed cholesterol values) as a function of body weight, where the definition of 'high' has no relation to body weight. In other words, the marker for what constitutes a 'high' cholesterol value is independent of body weight. What changes with body weight in this model is the odds that a cholesterol value would exceed this marker.
On the other hand, quantile regression is looking at how the 'marker' cholesterol values for which q% of the subjects with the same body weight in the underlying population have a higher cholesterol value vary as a function of body weight. You can think of these cholesterol values as markers for identifying what cholesterol values are 'high' - but in this case, each marker depends on the corresponding body weight; furthermore, the markers are assumed to change in a predictable fashion as the value of X changes (e.g., the markers tend to increase as X increases).
$endgroup$
1
$begingroup$
I agree with all that. Yet, there does seem to be a similarity - that is, both look at the qth quantile as a function of the same independent variables.
$endgroup$
– Peter Flom♦
8 hours ago
2
$begingroup$
Yes, but the difference is that one method looks at the unconditional quantile (i.e., logistic regression) while the other looks at the conditional quantile (i.e., quantile regression). Those two quantiles keep track of different things.
$endgroup$
– Isabella Ghement
8 hours ago
add a comment |
$begingroup$
For simplicity, assume you have a continuous dependent variable Y and a continuous predictor variable X.
Logistic Regression
If I understand your post correctly, your logistic regression will categorize Y into 0 and 1 based on the quantile of the (unconditional) distribution of Y. Specifically, the q-th quantile of the distribution of observed Y values will be computed and Ycat will be defined as 0 if Y is strictly less than this quantile and 1 if Y is greater than or equal to this quantile.
If the above captures your intent, then the logistic regression will model the odds of Y exceeding or being equal to the (observed) q-th quantile of the (unconditional) Y distribution as a function of X.
** Quantile Regression**
On the other hand, if you are performing a quantile regression of Y on X, you are focusing on modelling how the q-th quantile of the conditional distribution of Y given X changes as a function of X.
Logistic Regression versus Quantile Regression
It seems to me that these two procedures have totally different aims, since the first procedure (i.e., logistic regression) focuses on the q-th quantile of the unconditional distribution of Y, whereas the second procedure (i.e., quantile regression) focuses on the the q-th quantile of the conditional distribution of Y.
The unconditional distribution of Y is the
distribution of Y values (hence it ignores any
information about the X values).
The conditional distribution of Y given X is the
distribution of those Y values for which the values
of X are the same.
Illustrative Example
For illustration purposes, let's say Y = cholesterol and X = body weight.
Then logistic regression is modelling the odds of having a 'high' cholesterol value (i.e., greater than or equal to the q-th quantile of the observed cholesterol values) as a function of body weight, where the definition of 'high' has no relation to body weight. In other words, the marker for what constitutes a 'high' cholesterol value is independent of body weight. What changes with body weight in this model is the odds that a cholesterol value would exceed this marker.
On the other hand, quantile regression is looking at how the 'marker' cholesterol values for which q% of the subjects with the same body weight in the underlying population have a higher cholesterol value vary as a function of body weight. You can think of these cholesterol values as markers for identifying what cholesterol values are 'high' - but in this case, each marker depends on the corresponding body weight; furthermore, the markers are assumed to change in a predictable fashion as the value of X changes (e.g., the markers tend to increase as X increases).
$endgroup$
1
$begingroup$
I agree with all that. Yet, there does seem to be a similarity - that is, both look at the qth quantile as a function of the same independent variables.
$endgroup$
– Peter Flom♦
8 hours ago
2
$begingroup$
Yes, but the difference is that one method looks at the unconditional quantile (i.e., logistic regression) while the other looks at the conditional quantile (i.e., quantile regression). Those two quantiles keep track of different things.
$endgroup$
– Isabella Ghement
8 hours ago
add a comment |
$begingroup$
For simplicity, assume you have a continuous dependent variable Y and a continuous predictor variable X.
Logistic Regression
If I understand your post correctly, your logistic regression will categorize Y into 0 and 1 based on the quantile of the (unconditional) distribution of Y. Specifically, the q-th quantile of the distribution of observed Y values will be computed and Ycat will be defined as 0 if Y is strictly less than this quantile and 1 if Y is greater than or equal to this quantile.
If the above captures your intent, then the logistic regression will model the odds of Y exceeding or being equal to the (observed) q-th quantile of the (unconditional) Y distribution as a function of X.
** Quantile Regression**
On the other hand, if you are performing a quantile regression of Y on X, you are focusing on modelling how the q-th quantile of the conditional distribution of Y given X changes as a function of X.
Logistic Regression versus Quantile Regression
It seems to me that these two procedures have totally different aims, since the first procedure (i.e., logistic regression) focuses on the q-th quantile of the unconditional distribution of Y, whereas the second procedure (i.e., quantile regression) focuses on the the q-th quantile of the conditional distribution of Y.
The unconditional distribution of Y is the
distribution of Y values (hence it ignores any
information about the X values).
The conditional distribution of Y given X is the
distribution of those Y values for which the values
of X are the same.
Illustrative Example
For illustration purposes, let's say Y = cholesterol and X = body weight.
Then logistic regression is modelling the odds of having a 'high' cholesterol value (i.e., greater than or equal to the q-th quantile of the observed cholesterol values) as a function of body weight, where the definition of 'high' has no relation to body weight. In other words, the marker for what constitutes a 'high' cholesterol value is independent of body weight. What changes with body weight in this model is the odds that a cholesterol value would exceed this marker.
On the other hand, quantile regression is looking at how the 'marker' cholesterol values for which q% of the subjects with the same body weight in the underlying population have a higher cholesterol value vary as a function of body weight. You can think of these cholesterol values as markers for identifying what cholesterol values are 'high' - but in this case, each marker depends on the corresponding body weight; furthermore, the markers are assumed to change in a predictable fashion as the value of X changes (e.g., the markers tend to increase as X increases).
$endgroup$
For simplicity, assume you have a continuous dependent variable Y and a continuous predictor variable X.
Logistic Regression
If I understand your post correctly, your logistic regression will categorize Y into 0 and 1 based on the quantile of the (unconditional) distribution of Y. Specifically, the q-th quantile of the distribution of observed Y values will be computed and Ycat will be defined as 0 if Y is strictly less than this quantile and 1 if Y is greater than or equal to this quantile.
If the above captures your intent, then the logistic regression will model the odds of Y exceeding or being equal to the (observed) q-th quantile of the (unconditional) Y distribution as a function of X.
** Quantile Regression**
On the other hand, if you are performing a quantile regression of Y on X, you are focusing on modelling how the q-th quantile of the conditional distribution of Y given X changes as a function of X.
Logistic Regression versus Quantile Regression
It seems to me that these two procedures have totally different aims, since the first procedure (i.e., logistic regression) focuses on the q-th quantile of the unconditional distribution of Y, whereas the second procedure (i.e., quantile regression) focuses on the the q-th quantile of the conditional distribution of Y.
The unconditional distribution of Y is the
distribution of Y values (hence it ignores any
information about the X values).
The conditional distribution of Y given X is the
distribution of those Y values for which the values
of X are the same.
Illustrative Example
For illustration purposes, let's say Y = cholesterol and X = body weight.
Then logistic regression is modelling the odds of having a 'high' cholesterol value (i.e., greater than or equal to the q-th quantile of the observed cholesterol values) as a function of body weight, where the definition of 'high' has no relation to body weight. In other words, the marker for what constitutes a 'high' cholesterol value is independent of body weight. What changes with body weight in this model is the odds that a cholesterol value would exceed this marker.
On the other hand, quantile regression is looking at how the 'marker' cholesterol values for which q% of the subjects with the same body weight in the underlying population have a higher cholesterol value vary as a function of body weight. You can think of these cholesterol values as markers for identifying what cholesterol values are 'high' - but in this case, each marker depends on the corresponding body weight; furthermore, the markers are assumed to change in a predictable fashion as the value of X changes (e.g., the markers tend to increase as X increases).
edited 8 hours ago
answered 9 hours ago
Isabella GhementIsabella Ghement
7,846422
7,846422
1
$begingroup$
I agree with all that. Yet, there does seem to be a similarity - that is, both look at the qth quantile as a function of the same independent variables.
$endgroup$
– Peter Flom♦
8 hours ago
2
$begingroup$
Yes, but the difference is that one method looks at the unconditional quantile (i.e., logistic regression) while the other looks at the conditional quantile (i.e., quantile regression). Those two quantiles keep track of different things.
$endgroup$
– Isabella Ghement
8 hours ago
add a comment |
1
$begingroup$
I agree with all that. Yet, there does seem to be a similarity - that is, both look at the qth quantile as a function of the same independent variables.
$endgroup$
– Peter Flom♦
8 hours ago
2
$begingroup$
Yes, but the difference is that one method looks at the unconditional quantile (i.e., logistic regression) while the other looks at the conditional quantile (i.e., quantile regression). Those two quantiles keep track of different things.
$endgroup$
– Isabella Ghement
8 hours ago
1
1
$begingroup$
I agree with all that. Yet, there does seem to be a similarity - that is, both look at the qth quantile as a function of the same independent variables.
$endgroup$
– Peter Flom♦
8 hours ago
$begingroup$
I agree with all that. Yet, there does seem to be a similarity - that is, both look at the qth quantile as a function of the same independent variables.
$endgroup$
– Peter Flom♦
8 hours ago
2
2
$begingroup$
Yes, but the difference is that one method looks at the unconditional quantile (i.e., logistic regression) while the other looks at the conditional quantile (i.e., quantile regression). Those two quantiles keep track of different things.
$endgroup$
– Isabella Ghement
8 hours ago
$begingroup$
Yes, but the difference is that one method looks at the unconditional quantile (i.e., logistic regression) while the other looks at the conditional quantile (i.e., quantile regression). Those two quantiles keep track of different things.
$endgroup$
– Isabella Ghement
8 hours ago
add a comment |
$begingroup$
They won't be equal, and the reason is simple.
With quantile regression you want to model the quantile conditional of the independent variables. Your approach with logistic regression fits the marginal quantile.
$endgroup$
add a comment |
$begingroup$
They won't be equal, and the reason is simple.
With quantile regression you want to model the quantile conditional of the independent variables. Your approach with logistic regression fits the marginal quantile.
$endgroup$
add a comment |
$begingroup$
They won't be equal, and the reason is simple.
With quantile regression you want to model the quantile conditional of the independent variables. Your approach with logistic regression fits the marginal quantile.
$endgroup$
They won't be equal, and the reason is simple.
With quantile regression you want to model the quantile conditional of the independent variables. Your approach with logistic regression fits the marginal quantile.
answered 7 hours ago
FirebugFirebug
7,74923280
7,74923280
add a comment |
add a comment |
Thanks for contributing an answer to Cross Validated!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f401421%2fhow-does-quantile-regression-compare-to-logistic-regression-with-the-variable-sp%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
Could you show us any reasonable way even to compare the results of the two regressions? After all, unless you have something a little less general in mind, the coefficients of the regressors in these two models have entirely different meanings and interpretations, so in what sense are we to understand what you mean by "prefer"?
$endgroup$
– whuber♦
8 hours ago