Area Under the Curve - Variable and Log Transformed VariableHow to calculate sample size for comparing the...
Called into a meeting and told we are being made redundant (laid off) and "not to share outside". Can I tell my partner?
How spaceships determine each other's mass in space?
What is "desert glass" and what does it do to the PCs?
Dukha vs legitimate need
Is every open circuit a capacitor?
Under what conditions would I NOT add my Proficiency Bonus to a Spell Attack Roll (or Saving Throw DC)?
Is divide-by-zero a security vulnerability?
Does the US political system, in principle, allow for a no-party system?
What is the purpose of a disclaimer like "this is not legal advice"?
Preparing as much as possible of a cake in advance
Can you run a ground wire from stove directly to ground pole in the ground
Can a space-faring robot still function over a billion years?
The past tense for the quoting particle って
“I had a flat in the centre of town, but I didn’t like living there, so …”
What is Tony Stark injecting into himself in Iron Man 3?
Can a Mimic (container form) actually hold loot?
Convert an array of objects to array of the objects' values
Does the in-code argument passing conventions used on PDP-11's have a name?
PTIJ: Aliyot for the deceased
Quitting employee has privileged access to critical information
Is being socially reclusive okay for a graduate student?
Has a sovereign Communist government ever run, and conceded loss, on a fair election?
Was it really inappropriate to write a pull request for the company I interviewed with?
Why can't we use freedom of speech and expression to incite people to rebel against government in India?
Area Under the Curve - Variable and Log Transformed Variable
How to calculate sample size for comparing the area under the curve of two models?pattern of ROC curve and choice of AUCArea Under Curve ROC penalizes somehow models with too many explanatory variables?Area Under the ROC Curve, a simple questionArea Under the ROC Curve: Comparing identification performance between two values of the same variabletwo questions; how to interpret the AUROC (area under the ROC curve)Area Under the Curve physical meaningArea Under The Receiver Operating - incompatible explanationsQ: Possible to optimize for area under the precision-recall curve in glmnet logistic regression?How to distinguish overfitting and underfitting from the ROC AUC curve?
$begingroup$
I have a situation where I am fitting two simple logistic regression models - one model with the variable of interest included as the only predictor, and the other model with the log of the variable of interest included as the only predictor. Both models have the same Area Under the Curve, and I would like to know how to explain why this occurs. I am sure this is not due to chance, but rather has something to do with how AUC is calculated, and it's interpretation.
logistic roc auc
asked 4 hours ago
APKAPK
1278
$endgroup$
add a comment |
$begingroup$
I have a situation where I am fitting two simple logistic regression models - one model with the variable of interest included as the only predictor, and the other model with the log of the variable of interest included as the only predictor. Both models have the same Area Under the Curve, and I would like to know how to explain why this occurs. I am sure this is not due to chance, but rather has something to do with how AUC is calculated, and it's interpretation.
logistic roc auc
asked 4 hours ago
APKAPK
1278
$endgroup$
add a comment |
$begingroup$
I have a situation where I am fitting two simple logistic regression models - one model with the variable of interest included as the only predictor, and the other model with the log of the variable of interest included as the only predictor. Both models have the same Area Under the Curve, and I would like to know how to explain why this occurs. I am sure this is not due to chance, but rather has something to do with how AUC is calculated, and it's interpretation.
logistic roc auc
asked 4 hours ago
APKAPK
1278
$endgroup$
I have a situation where I am fitting two simple logistic regression models - one model with the variable of interest included as the only predictor, and the other model with the log of the variable of interest included as the only predictor. Both models have the same Area Under the Curve, and I would like to know how to explain why this occurs. I am sure this is not due to chance, but rather has something to do with how AUC is calculated, and it's interpretation.
logistic roc auc
logistic roc auc
asked 4 hours ago
APKAPK
1278
asked 4 hours ago
APKAPK
1278
edited 3 hours ago
APK
asked 4 hours ago
APKAPK
1278
asked 4 hours ago
APKAPK
1278
asked 4 hours ago
APKAPK
1278
1278
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
It is because the AUC is invariant to monotonic changes of variable, of which the log-transform is a special case. The AUC is the probability that a randomly selected case has a higher risk than a control. While the raw difference in risk may not be the same for those two models, the case will still have a higher risk when calculated using either the log-transformed predictor or the untransformed predictor.
It should give us some pause and doubt about AUC that it makes no use whatsoever of the actual risk predicted by the model, but rather the ordering of groups according to a predicted risk (be it arbitrary or otherwise). The axes on a ROC are just sensitivity and 1-specificity.
answered 4 hours ago
AdamOAdamO
33.8k263140
$endgroup$
$begingroup$
Thanks AdamO. Great explanation.
$endgroup$
– APK
3 hours ago
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%2f396245%2farea-under-the-curve-variable-and-log-transformed-variable%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
It is because the AUC is invariant to monotonic changes of variable, of which the log-transform is a special case. The AUC is the probability that a randomly selected case has a higher risk than a control. While the raw difference in risk may not be the same for those two models, the case will still have a higher risk when calculated using either the log-transformed predictor or the untransformed predictor.
It should give us some pause and doubt about AUC that it makes no use whatsoever of the actual risk predicted by the model, but rather the ordering of groups according to a predicted risk (be it arbitrary or otherwise). The axes on a ROC are just sensitivity and 1-specificity.
answered 4 hours ago
AdamOAdamO
33.8k263140
$endgroup$
$begingroup$
Thanks AdamO. Great explanation.
$endgroup$
– APK
3 hours ago
add a comment |
$begingroup$
It is because the AUC is invariant to monotonic changes of variable, of which the log-transform is a special case. The AUC is the probability that a randomly selected case has a higher risk than a control. While the raw difference in risk may not be the same for those two models, the case will still have a higher risk when calculated using either the log-transformed predictor or the untransformed predictor.
It should give us some pause and doubt about AUC that it makes no use whatsoever of the actual risk predicted by the model, but rather the ordering of groups according to a predicted risk (be it arbitrary or otherwise). The axes on a ROC are just sensitivity and 1-specificity.
answered 4 hours ago
AdamOAdamO
33.8k263140
$endgroup$
$begingroup$
Thanks AdamO. Great explanation.
$endgroup$
– APK
3 hours ago
add a comment |
$begingroup$
It is because the AUC is invariant to monotonic changes of variable, of which the log-transform is a special case. The AUC is the probability that a randomly selected case has a higher risk than a control. While the raw difference in risk may not be the same for those two models, the case will still have a higher risk when calculated using either the log-transformed predictor or the untransformed predictor.
It should give us some pause and doubt about AUC that it makes no use whatsoever of the actual risk predicted by the model, but rather the ordering of groups according to a predicted risk (be it arbitrary or otherwise). The axes on a ROC are just sensitivity and 1-specificity.
answered 4 hours ago
AdamOAdamO
33.8k263140
$endgroup$
It is because the AUC is invariant to monotonic changes of variable, of which the log-transform is a special case. The AUC is the probability that a randomly selected case has a higher risk than a control. While the raw difference in risk may not be the same for those two models, the case will still have a higher risk when calculated using either the log-transformed predictor or the untransformed predictor.
It should give us some pause and doubt about AUC that it makes no use whatsoever of the actual risk predicted by the model, but rather the ordering of groups according to a predicted risk (be it arbitrary or otherwise). The axes on a ROC are just sensitivity and 1-specificity.
answered 4 hours ago
AdamOAdamO
33.8k263140
answered 4 hours ago
AdamOAdamO
33.8k263140
answered 4 hours ago
AdamOAdamO
33.8k263140
answered 4 hours ago
AdamOAdamO
33.8k263140
33.8k263140
$begingroup$
Thanks AdamO. Great explanation.
$endgroup$
– APK
3 hours ago
add a comment |
$begingroup$
Thanks AdamO. Great explanation.
$endgroup$
– APK
3 hours ago
$begingroup$
Thanks AdamO. Great explanation.
$endgroup$
– APK
3 hours ago
$begingroup$
Thanks AdamO. Great explanation.
$endgroup$
– APK
3 hours ago
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%2f396245%2farea-under-the-curve-variable-and-log-transformed-variable%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
