Estimating Missing Dependent Variables
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Estimating Missing Dependent Variables
 
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I want to use the results of a logistic regression to estimate values
for cases where the dependent variable is missing. I have a dataset which has 10,000 cases with dependent variables and another 10,000 cases that do not. How can I do this? I'm hoping to avoid writing a long mathematical formula as my coefficients and significant variables are going to change often. Aaron ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: Estimating Missing Dependent Variables
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Logistic Regression typically estimates the odds that a binary variable
turns out to be 0 or 1. It does not estimate whether in a particular case the value would be 0 or 1. In some applications it is often found that practitioners use a cutoff point to assign a predicted value to the dependent variable, e.g. assign the value 1 to a particular case if the estimated probability of the outcome being 1 is higher than 0.5, and 0 otherwise. In your case, you may estimate the logistic equation for the first set of cases, and then apply the same equation to the second set, to generate the probability of the event for each case. SPSS allows you to save this probability as a new variable in your dataset, with the SAVE subcommand of LOGREG. This is common practice, and would raise few eyebrows. However, I think it is wrong in a philosophical level. Probability, I think, is not about individual cases but about groups or populations. When you predict that people with Agegroup 20-29 and sex=1 and education=3 would have probability=0.7 of voting for candidate Obama, you are simply saying that 70% of all people with those characteristics will probably vote for Obama, but you know nothing about the vote of Mrs Jones or Mr Smith, even if they share all those characteristics: they might be in the 70% voting for Obama, or in the other 30%. Just the same, you know there is 4/6 probability that a die turns out value greater than 3, but you know nothing at all about the next throw: it may show any number from 1 to 6. Its "probability" is indeterminate: it will turn into a concrete number (with probability 1) or remain indeterminate (all numbers possible). The probability just says that 4/6 or 2/3 out of any large number of dice throws would be a number larger than 3. You are speaking of large numbers, and that's the reason why the fundamental theorem of statistics is known to its buddies as the Law of Large Numbers. All statistics is about large numbers. For statistitians, individuals are disposable, and indeterminate. This has also practical implications. Suppose you are allocating fellowships at college entrance, based on a number of variables predicting college success. Your donors do not want the money wasted on college dropouts. So you analyse past students, with and without fellowships, and come up with an log reg equation to predict the probability of scholarly success, thus allowing you to give the money only to the best prospects. You will keep your donors happy, until they discover you rejected Albert Einstein, a terrible prospect by any measure at the age of 17. Instead you accepted a lot of dull guys able to approve SAT after SAT, most of which will end up as clerks or salesmen, will never discover anything more trascendental than a cheating wife or husband, and will quickly forget everything they ever learnt in college about matter or energy. Your equation, in short, tells you the truth for relatively large groups of people sharing certain features, but not necessarily for specific cases. Hector -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Aaron Kreider Sent: 08 June 2009 17:04 To: [hidden email] Subject: Estimating Missing Dependent Variables I want to use the results of a logistic regression to estimate values for cases where the dependent variable is missing. I have a dataset which has 10,000 cases with dependent variables and another 10,000 cases that do not. How can I do this? I'm hoping to avoid writing a long mathematical formula as my coefficients and significant variables are going to change often. Aaron ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: Estimating Missing Dependent Variables
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Jon, I will repeat your comments separately from my
main text for the sake of clarity. 1. Regarding my idea that probability is about groups,
and not about individuals, you write: " So then, how would you do prediction
for individual cases, be they people, countries, or any other observation
unit? If faced with a decision problem, would you disallow statistical
models altogether?" Jon, it is different in the case of linear regression.
Log reg does not predict individual values, but probabilities. My point is that
probabilities are essentially a property of groups (groups of events,
populations, and so on). There are certain concepts of probability (e.g.
Finetti’s subjective concept of probability) that may assign something
called "probability" to
a single case, but the most accepted meaning of probability is "frequentist", identifying
probability with relative frequency of an event or attribute within a given
population, group or set. In linear (or for that matter nonlinear) regression
one predicts the value of a variable for each individual case, which is
modelled as the sum of a linear/nonlinear function plus a random error, using
an algorithm that minimizes the sum of the squared errors. In such case you are
actually estimating individual values. 2. Later I mention the example of a model predicting
college success based on SAT, and failing to select Einstein. You reply : « Of course, but it was just an example. Even if you
include creativity or whatever, what you are doing in the example (assigning
scholarships to candidates) is TRYING TO MINIMIZE THE PROPORTION OF FAILURES in
the GROUP of people you are analyzing. You are not predicting the outcome of
individual cases. Within a a subgroup with a certain probability of success
(e.g. people sharing the same gender, education, SAT score, creativity, and all
other predictors), some individuals will ultimately succeed, some will fail,
and the information you have is exactly the same for all of them : as far
as you know, the individual outcome WITHIN THE GROUP is indeterminate. That was
my point. The probability is predicated of the group, not of the individual. The
Dean of Admissions will probably minimize the number or proportion of dropouts among
students granted a scholarship, but (1) cannot tell in advance who among the beneficiaries
will drop out, and (b) cannot tell in advance whether there is someone else who
was not a beneficiary but would have been (with hindsight) a better choice. He
deals with groups, not individuals. I hope this clarifies the issue. Hector -----Original Message----- Hector, I've made a few comments below. -----Original Message----- From: SPSSX(r) Discussion Sent: Monday, June 08, 2009 3:13 PM To: [hidden email] Subject: Re: Logistic Regression typically estimates the odds that
a binary variable turns out to be 0 or 1. It does not estimate whether
in a particular case the value would be 0 or 1. In some applications it is often found that
practitioners use a cutoff point to assign a predicted value to the dependent variable,
e.g. assign the value 1 to a particular case if the estimated probability of
the outcome being 1 is higher than 0.5, and 0 otherwise. In your case, you may estimate the logistic equation
for the first set of cases, and then apply the same equation to the second
set, to generate the probability of the event for each case. SPSS allows
you to save this probability as a new variable in your dataset, with
the SAVE subcommand of LOGREG. This is common practice, and would raise few eyebrows.
However, I think it is wrong in a philosophical level. Probability, I
think, is not about individual cases but about groups or populations. When
you predict that people with Agegroup 20-29 and sex=1 and education=3
would have probability=0.7 of voting for candidate Obama, you are
simply saying that 70% of all people with those characteristics will
probably vote for Obama, but you know nothing about the vote of Mrs Jones or Mr
Smith, even if they share all those characteristics: they might be in the
70% voting for Obama, or in the other 30%. Just the same, you know there is
4/6 probability that a die turns out value greater than 3, but you know
nothing at all about the next throw: it may show any number from 1 to 6. Its
"probability" is indeterminate: it will turn into a concrete number
(with probability 1) or remain indeterminate (all numbers possible). The
probability just says that 4/6 or 2/3 out of any large number of dice throws
would be a number larger than 3. You are speaking of large numbers, and that's
the reason why the fundamental theorem of statistics is known to its
buddies as the Law of Large Numbers. All statistics is about large numbers.
For statistitians, individuals are disposable, and indeterminate. So then, how would you do prediction for individual
cases, be they people, countries, or any other observation unit? If faced
with a decision problem, would you disallow statistical models altogether? This has also practical implications. Suppose you are
allocating fellowships at college entrance, based on a number of variables
predicting college success. Your donors do not want the money wasted on
college dropouts. So you analyse past students, with and without
fellowships, and come up with an log reg equation to predict the probability of
scholarly success, thus allowing you to give the money only to the best
prospects. You will keep your donors happy, until they discover
you rejected Albert Einstein, a terrible prospect by any measure at the
age of 17. Instead you accepted a lot of dull guys able to approve SAT after
SAT, most of which will end up as clerks or salesmen, will never discover
anything more trascendental than a cheating wife or husband, and
will quickly forget everything they ever learnt in college about matter or
energy. Your equation, in short, tells you the truth for
relatively large groups of people sharing certain features, but not necessarily
for specific cases. Regards, Jon Hector -----Original Message----- From: SPSSX(r) Discussion Aaron Kreider Sent: 08 June 2009 17:04 To: [hidden email] Subject: Estimating Missing Dependent Variables I want to use the results of a logistic regression to
estimate values for cases where the dependent variable is missing. I
have a dataset which has 10,000 cases with dependent variables and
another 10,000 cases that do not. How can I do this? I'm hoping to avoid writing a long mathematical
formula as my coefficients and significant variables are going to
change often. Aaron ===================== To manage your subscription to SPSSX-L, send a message
to [hidden email] (not to SPSSX-L), with no
body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send
the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message
to [hidden email] (not to SPSSX-L), with no
body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send
the command INFO REFCARD |
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From: SPSSX(r)
Discussion [mailto:[hidden email]] On
Behalf Of Hector Maletta Jon, I will repeat your comments separately from my
main text for the sake of clarity. 1. Regarding my idea that probability is about groups,
and not about individuals, you write: " So then, how would you do prediction
for individual cases, be they people, countries, or any other observation
unit? If faced with a decision problem, would you disallow statistical
models altogether?" Jon, it is different in the case of linear regression.
Log reg does not predict individual values, but probabilities. My point is that
probabilities are essentially a property of groups (groups of events,
populations, and so on). There are certain concepts of probability (e.g.
Finetti’s subjective concept of probability) that may assign something
called "probability" to
a single case, but the most accepted meaning of probability is "frequentist", identifying
probability with relative frequency of an event or attribute within a given
population, group or set. In linear (or for that matter nonlinear) regression one
predicts the value of a variable for each individual case, which is modelled as
the sum of a linear/nonlinear function plus a random error, using an algorithm
that minimizes the sum of the squared errors. In such case you are actually
estimating individual values. [>>>Peck,
Jon] Well, you are estimating expected values in ordinary regression. p
is also an estimated expected value (of a 0/1 outcome). But in both cases
that still leaves the decision problem to be solved. Who would you admit?
Or, in classic terms, given the probability of rain, when would you carry an
umbrella? [>>>Peck, Jon] [snip] |
Re: Estimating Missing Dependent Variables
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1. Regarding my idea that probability is about groups,
and not about individuals, Jon Peck
wrote: " Jon, it is different in the case of linear regression.
Log reg does not predict individual values, but probabilities. My point is that
probabilities are essentially a property of groups (groups of events,
populations, and so on). There are certain concepts of probability (e.g.
Finetti’s subjective concept of probability) that may assign something
called "probability" to
a single case, but the most accepted meaning of probability is "frequentist", identifying
probability with relative frequency of an event or attribute within a given
population, group or set. In linear (or for that matter nonlinear) regression
one predicts the value of a variable for each individual case, which is
modelled as the sum of a linear/nonlinear function plus a random error, using
an algorithm that minimizes the sum of the squared errors. In such case you are
actually estimating individual values. Jon, the probability p is
not an expected value of the outcome. It is a probability. The expected values
are only two : call them 0 or 1, or A and B, or whatever alphanumeric symbols
you choose for the two outcomes. (either your event happens or it does not). On
the other hand p
is a real number between 0 or 1. It is the probability of getting one of the
values, say the value A (the plane crashes in mid Atlantic, or this candidate
drops out of college). The term probability is best interpreted as « the
proportion of cases with the outcome A» within a given set of cases
with such and such characteristics Now, regarding decision,
that’s a different story altogether. Once you know the probability of an
event, you can take a number of possible decisions about it (not only one), and
your decision can be based on any of a number of possible criteria. If you, for
instance, adopt a (possibly arbitrary) cutoff point like p=0.5, and assign all
cases with p >0.5 to Group A and all others to Group
not-A; but that would be, well, your decision. You may assign a cutoff value
for some decisions, and a different cutoff value for other decisions. Someone
else could adopt some other criterion for each decision, such as p>0.9 or
p>0.2 instead of your 0.5, and there might be some valid reasons for any
such decision rules. For instance, you may adopt the prudential decision to
build a costly hurricane levee in Do you agree with this? Hector |
Re: Estimating Missing Dependent Variables
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In reply to this post by Peck, Jon
Moreover, Jon, Besides the decision question being different
from the question of meaning and estimation of the probability, in any case
your decision will affect entire groups or categories of people; you would be
unable to say anything about how the die will roll in each particular case
within each category of people sharing the same probability. Some people with
high probability will not suffer the event, while some with very low
probability will. You, for instance, may decide to give a college
scholarship (or student loan) to all candidates whose predicted probability of
college success is over 0.8. Some of them will actually succeed, some will not,
and you do not have a clue about which is which. By the same token, you as a
doctor should decide on giving or not giving Treatment A to patients suffering
certain painful disease which (if untreated) would probably kill them in a few
years. The treatment is effective in most cases, but in some cases it has lethal
side effects that would kill the patient instantly; that unfortunate outcome is
never certain: its probability p depends on some predictors. You (or the medical
profession) give the treatment to all patients whose p is lower than, say,
1%. But you do not know in advance whether your next patient (estimated p=0.009) will be
cured, or she is instead a member of the unlucky lot that will be instantly killed
by the treatment. It’s kinda Russian roulette at that point, only the gun
has 100 holes, of which 99 are empty and one has a bullet. Knowing the
probability of a category of people tells you nothing about the individual fate
of each patient, just as (in Russian roulette) knowing that you have 1 chance
in 6 tells you nothing how things will turn out the next time you pull the
trigger. Hector From: Hector
Maletta 1. Regarding my idea that probability is about groups,
and not about individuals, Jon Peck
wrote: " Jon, it is different in the case of linear regression.
Log reg does not predict individual values, but probabilities. My point is that
probabilities are essentially a property of groups (groups of events,
populations, and so on). There are certain concepts of probability (e.g.
Finetti’s subjective concept of probability) that may assign something
called "probability" to
a single case, but the most accepted meaning of probability is "frequentist", identifying
probability with relative frequency of an event or attribute within a given
population, group or set. In linear (or for that matter nonlinear) regression
one predicts the value of a variable for each individual case, which is
modelled as the sum of a linear/nonlinear function plus a random error, using
an algorithm that minimizes the sum of the squared errors. In such case you are
actually estimating individual values. Jon, the probability p is
not an expected value of the outcome. It is a probability. The expected values
are only two : call them 0 or 1, or A and B, or whatever alphanumeric
symbols you choose for the two outcomes. (either your event happens or it does
not). On the other hand p
is a real number between 0 or 1. It is the probability of getting one of the
values, say the value A (the plane crashes in mid Atlantic, or this candidate
drops out of college). The term probability is best interpreted as
« the proportion of cases with the outcome A» within a
given set of cases with such and such characteristics Now, regarding decision,
that’s a different story altogether. Once you know the probability of an
event, you can take a number of possible decisions about it (not only one), and
your decision can be based on any of a number of possible criteria. If you, for
instance, adopt a (possibly arbitrary) cutoff point like p=0.5, and assign all
cases with p >0.5 to Group A and all others to Group
not-A; but that would be, well, your decision. You may assign a cutoff value
for some decisions, and a different cutoff value for other decisions. Someone
else could adopt some other criterion for each decision, such as p>0.9 or
p>0.2 instead of your 0.5, and there might be some valid reasons for any
such decision rules. For instance, you may adopt the prudential decision to
build a costly hurricane levee in Do you agree with this? Hector |
Re: Estimating Missing Dependent Variables
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In reply to this post by Aaron Kreider
Dear Aaron,
I'm not sure whether this is the easiest option with SPSS, but you could 1) merge your files with ADD FILES 2) Compute near zero weights for cases with missing dependents (in the example: 1E-25). If your data are unweighted, assign unity case weights to the other cases. Otherwise, copy the existing weights for those 3) replace the missing dependent values with zeros 4) Weight your sample 5) Run Logistic regression and save the predicted probabilities. The trick is that the cases with missing dependent values will get predicted probabilities because the missing values have been replaced with zeros. However, because they've near zero weight, they won't influence the regression results substantially. *A completely different approach could be to use OMS to create a new dataset containing the betas and use string manipulations to convert this into syntax *that uses only independent variables and the regression equation to calculate predicted probabilities. For example, try: ***Create testdata. DATAS CLO ALL. NEW FIL. SET SEED 123456. INP PRO. LOOP #I=1 to 15. COMP ID=#I. END CASE. END LOOP. END FIL. END INP PRO. EXE. COMP Dep=RV.BER(.5). DO REP Vars=Ind_1 to Ind_4. COMP Vars=RV.UNI(1,10). END REP. DO IF $casenum GE 11. RECOD Dep (ELSE=SYSMIS). END IF. EXE. ***End create data. ***Regression without incomplete cases. LOGISTIC REGRESSION Dep /METHOD = ENTER Ind_1 Ind_2 Ind_3 Ind_4 /SAVE = PRED /CRITERIA = PIN(.05) POUT(.10) ITERATE(20) CUT(.5) . ***Assigning case weights. COMP Weight=1. DO IF MIS(Dep)=1. COMP Dep=0. COMP Weight=1E-25. END IF. EXE. WEI by Weight. ***Regression with completed cases. LOGISTIC REGRESSION Dep /METHOD = ENTER Ind_1 Ind_2 Ind_3 Ind_4 /SAVE = PRED /CRITERIA = PIN(.05) POUT(.10) ITERATE(20) CUT(.5) . ***Replace previously missing values with predicted probabilities if desired. DO IF Weight=1E-25. COMP Dep=PRE_2. END IF. EXE. > Date: Mon, 8 Jun 2009 16:03:50 -0400 > From: [hidden email] > Subject: Estimating Missing Dependent Variables > To: [hidden email] > > I want to use the results of a logistic regression to estimate values > for cases where the dependent variable is missing. I have a dataset > which has 10,000 cases with dependent variables and another 10,000 cases > that do not. How can I do this? > > I'm hoping to avoid writing a long mathematical formula as my > coefficients and significant variables are going to change often. > > Aaron > > ===================== > To manage your subscription to SPSSX-L, send a message to > [hidden email] (not to SPSSX-L), with no body text except the > command. To leave the list, send the command > SIGNOFF SPSSX-L > For a list of commands to manage subscriptions, send the command > INFO REFCARD Express yourself instantly with MSN Messenger! MSN Messenger |
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In reply to this post by Hector Maletta
Hello,
I have a data sequence problem that seems to be beyond my syntax ability. I hope you can help. This is this page view data I currently have. EntryPage NextPage Page PreviousPage ExitPage Page C Page F Page D Page F Page C Page E Page G Page A Page F Page C Page G Page A Page C Page F Page C Page A Page C Page F Page C Page D Page E Page G Page F Page C Page F Page D Page E Page F I want to get it to look like this which would identify the sequence of page views. EntryPage NextPage Page PreviousPage ExitPage Page C Page C Page F Page C Page G Page A Page C Page F Page C Page E Page G Page A Page F Page C Page D Page E Page G Page F Page C Page F Page D Page E Page F Page C Page F Page D Page F This is driving me crazy because I cannot get the original file in the right order and it is not a quick sort to identify the sequence. Thanks for your help. RG Rodrigo A. Guerrero | Director Of Marketing Research and Analysis | The Scooter Store | 830.627.4317 The information transmitted is intended only for the addressee(s) and may contain confidential or privileged material, or both. Any review, receipt, dissemination or other use of this information by non-addressees is prohibited. If you received this in error or are a non-addressee, please contact the sender and delete the transmitted information. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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Dear list,
I need to produce frequency reports for about 300 tables where the inforamtion (counts and simple percentages) is presented in rows instead of columns, as the default. Then I need to move that into Excel as a table so it can be edited some more. It would be great if I could just somehow turn this into a data file. Using SPSS V15.
Years ago I used scrips and macros but those skills are now quite rusty and this report is due yesterday!
Any help is greatly appreciated.
John
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In reply to this post by Guerrero, Rodrigo
Rodrigo,
Two questions. 1) It looks like you have six columns of data but only five column labels. Did you omit something or am I missing something? 2) What is the set of rules that you used to transform the input data set to the output dataset? I don't get it but then I've never worked with page view sequence data. Gene Maguin >>I have a data sequence problem that seems to be beyond my syntax ability. I hope you can help. This is this page view data I currently have. EntryPage NextPage Page PreviousPage ExitPage Page C Page F Page D Page F Page C Page E Page G Page A Page F Page C Page G Page A Page C Page F Page C Page A Page C Page F Page C Page D Page E Page G Page F Page C Page F Page D Page E Page F I want to get it to look like this which would identify the sequence of page views. EntryPage NextPage Page PreviousPage ExitPage Page C Page C Page F Page C Page G Page A Page C Page F Page C Page E Page G Page A Page F Page C Page D Page E Page G Page F Page C Page F Page D Page E Page F Page C Page F Page D Page F This is driving me crazy because I cannot get the original file in the right order and it is not a quick sort to identify the sequence. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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In reply to this post by Hector Maletta
A few more
last comments below. From: SPSSX(r)
Discussion [mailto:[hidden email]] On
Behalf Of Hector Maletta Moreover, Jon, Besides the decision question being
different from the question of meaning and estimation of the probability, in
any case your decision will affect entire groups or categories of people; you
would be unable to say anything about how the die will roll in each particular
case within each category of people sharing the same probability. Some people
with high probability will not suffer the event, while some with very low
probability will. [>>>Peck,
Jon] And in the same way, in an ordinary conditional expectation model, some
units will have higher than expected outcomes and some lower, and a regression
equation cannot say any more about which are which given equal expectation. You, for instance, may decide to give a
college scholarship (or student loan) to all candidates whose predicted
probability of college success is over 0.8. Some of them will actually succeed,
some will not, and you do not have a clue about which is which. By the same
token, you as a doctor should decide on giving or not giving Treatment A to
patients suffering certain painful disease which (if untreated) would probably
kill them in a few years. The treatment is effective in most cases, but in some
cases it has lethal side effects that would kill the patient instantly; that
unfortunate outcome is never certain: its probability p depends on some
predictors. You (or the medical profession) give the treatment to all
patients whose p
is lower than, say, 1%. But you do not know in advance whether your next
patient (estimated p=0.009)
will be cured, or she is instead a member of the unlucky lot that will be
instantly killed by the treatment. It’s kinda Russian roulette at that
point, only the gun has 100 holes, of which 99 are empty and one has a bullet.
Knowing the probability of a category of people tells you nothing about the
individual fate of each patient, just as (in Russian roulette) knowing that you
have 1 chance in 6 tells you nothing how things will turn out the next time you
pull the trigger. [>>>Peck,
Jon] Isn't it equivalent to say that a very good p function – in the
extreme predicting 0 or 1 probabilities, is like a regression equation with a
very high fit/small error? If there is inherent randomness, no model is
going to capture that (but some vigorous overfitting might make it seem
otherwise L) Hector |
Re: Estimating Missing Dependent Variables
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Last comments indeed. In all statistical
estimates there is a margin of error, granted, Jon. But in regression you
actually estimate the value, and your THEORETICAL model includes the error:
y=a+bX+e. The actual event is SUPPOSED to obey two kinds of causes, one
systematic (X) and one random (e). Thus you obtain and estimate of the expected
value (a+bX) and an estimate of the error component (e); the least squares
algorithm chooses “a” and “b” such that the sum of the
squared error components “e” is minimized. Instead in logistic regression your
theoretical model for an individual is totally different. It is deterministic. Either
she is in State A or State B. No middle way. Either she drops out of college or
she doesn’t. Either she is alive or she is dead. There is no “probability”
or “error” in the model for individuals, only the two stark
discrete states. What you predict, what you deal about indeed, is not the state
of each individual, but the probability (read: EXPECTED RELATIVE FREQUENCY) of one
of the states IN A GROUP OF INDIVIDUALS. Your margin of error would be in this
relative frequency: for instance when you throw 100 coins, the expected
frequency of tails is 50, but perhaps you get 49 or 52, and that is your margin
of error. By the same token, if your model predicts (for some group sharing
certain combination of predictors’ values) a probability of 0.20, perhaps
the proportion of actual events turns out to be 0.22 or 0.18. The error is in
the prediction of the relative frequency, not in the estimation of each individual
outcome, because you are not predicting individual outcomes in that kind of
models. Hector From: A few more
last comments below. From: SPSSX(r)
Discussion Moreover, Jon, Besides the decision question being
different from the question of meaning and estimation of the probability, in
any case your decision will affect entire groups or categories of people; you
would be unable to say anything about how the die will roll in each particular
case within each category of people sharing the same probability. Some people
with high probability will not suffer the event, while some with very low
probability will. You, for instance, may decide to give a
college scholarship (or student loan) to all candidates whose predicted
probability of college success is over 0.8. Some of them will actually succeed,
some will not, and you do not have a clue about which is which. By the same
token, you as a doctor should decide on giving or not giving Treatment A to
patients suffering certain painful disease which (if untreated) would probably
kill them in a few years. The treatment is effective in most cases, but in some
cases it has lethal side effects that would kill the patient instantly; that
unfortunate outcome is never certain: its probability p depends on some
predictors. You (or the medical profession) give the treatment to all
patients whose p
is lower than, say, 1%. But you do not know in advance whether your next
patient (estimated p=0.009)
will be cured, or she is instead a member of the unlucky lot that will be
instantly killed by the treatment. It’s kinda Russian roulette at that
point, only the gun has 100 holes, of which 99 are empty and one has a bullet.
Knowing the probability of a category of people tells you nothing about the
individual fate of each patient, just as (in Russian roulette) knowing that you
have 1 chance in 6 tells you nothing how things will turn out the next time you
pull the trigger. Hector |
Re: Estimating Missing Dependent Variables
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Hector,
I think thing are not as clear cut as you say. In a logistic model the probabilities come from a logistic distribution - forget about error it only confuses things. Estimation involves fitting a logistic distribution to get estimated probabilities. Similarly in a normal model the data values themselves are normally distributed and estimation involves fitting a normal dist to the y values. For bernoulli data as you describe the key thing is that logit transforms the [0,1] probability scale [-inf, +inf]. For normal data this transformation is the identity. Gerard Hector Maletta <hmaletta@fiberte l.com.ar> To Sent by: [hidden email] "SPSSX(r) cc Discussion" <SPSSX-L@LISTSERV Subject .UGA.EDU> Re: Estimating Missing Dependent Variables 10/06/2009 19:28 Please respond to Hector Maletta <hmaletta@fiberte l.com.ar> Last comments indeed. In all statistical estimates there is a margin of error, granted, Jon. But in regression you actually estimate the value, and your THEORETICAL model includes the error: y=a+bX+e. The actual event is SUPPOSED to obey two kinds of causes, one systematic (X) and one random (e). Thus you obtain and estimate of the expected value (a+bX) and an estimate of the error component (e); the least squares algorithm chooses “a” and “b” such that the sum of the squared error components “e” is minimized. Instead in logistic regression your theoretical model for an individual is totally different. It is deterministic. Either she is in State A or State B. No middle way. Either she drops out of college or she doesn’t. Either she is alive or she is dead. There is no “probability” or “error” in the model for individuals, only the two stark discrete states. What you predict, what you deal about indeed, is not the state of each individual, but the probability (read: EXPECTED RELATIVE FREQUENCY) of one of the states IN A GROUP OF INDIVIDUALS. Your margin of error would be in this relative frequency: for instance when you throw 100 coins, the expected frequency of tails is 50, but perhaps you get 49 or 52, and that is your margin of error. By the same token, if your model predicts (for some group sharing certain combination of predictors’ values) a probability of 0.20, perhaps the proportion of actual events turns out to be 0.22 or 0.18. The error is in the prediction of the relative frequency, not in the estimation of each individual outcome, because you are not predicting individual outcomes in that kind of models. Hector From: Peck, Jon [mailto:[hidden email]] Sent: 10 June 2009 13:55 To: Hector Maletta; [hidden email] Subject: RE: Re: [SPSSX-L] Estimating Missing Dependent Variables A few more last comments below. From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Hector Maletta Sent: Monday, June 08, 2009 9:46 PM To: [hidden email] Subject: Re: [SPSSX-L] Estimating Missing Dependent Variables Moreover, Jon, Besides the decision question being different from the question of meaning and estimation of the probability, in any case your decision will affect entire groups or categories of people; you would be unable to say anything about how the die will roll in each particular case within each category of people sharing the same probability. Some people with high probability will not suffer the event, while some with very low probability will. [>>>Peck, Jon] And in the same way, in an ordinary conditional expectation model, some units will have higher than expected outcomes and some lower, and a regression equation cannot say any more about which are which given equal expectation. You, for instance, may decide to give a college scholarship (or student loan) to all candidates whose predicted probability of college success is over 0.8. Some of them will actually succeed, some will not, and you do not have a clue about which is which. By the same token, you as a doctor should decide on giving or not giving Treatment A to patients suffering certain painful disease which (if untreated) would probably kill them in a few years. The treatment is effective in most cases, but in some cases it has lethal side effects that would kill the patient instantly; that unfortunate outcome is never certain: its probability p depends on some predictors. You (or the medical profession) give the treatment to all patients whose p is lower than, say, 1%. But you do not know in advance whether your next patient (estimated p=0.009) will be cured, or she is instead a member of the unlucky lot that will be instantly killed by the treatment. It’s kinda Russian roulette at that point, only the gun has 100 holes, of which 99 are empty and one has a bullet. Knowing the probability of a category of people tells you nothing about the individual fate of each patient, just as (in Russian roulette) knowing that you have 1 chance in 6 tells you nothing how things will turn out the next time you pull the trigger. [>>>Peck, Jon] Isn't it equivalent to say that a very good p function – in the extreme predicting 0 or 1 probabilities, is like a regression equation with a very high fit/small error? If there is inherent randomness, no model is going to capture that (but some vigorous overfitting might make it seem otherwise L) Hector ********************************************************************************** The information transmitted is intended only for the person or entity to which it is addressed and may contain confidential and/or privileged material. Any review, retransmission, dissemination or other use of, or taking of any action in reliance upon, this information by persons or entities other than the intended recipient is prohibited. If you received this in error, please contact the sender and delete the material from any computer. It is the policy of the Department of Justice, Equality and Law Reform and the Agencies and Offices using its IT services to disallow the sending of offensive material. Should you consider that the material contained in this message is offensive you should contact the sender immediately and also mailminder[at]justice.ie. Is le haghaidh an duine nó an eintitis ar a bhfuil sí dírithe, agus le haghaidh an duine nó an eintitis sin amháin, a bheartaítear an fhaisnéis a tarchuireadh agus féadfaidh sé go bhfuil ábhar faoi rún agus/nó faoi phribhléid inti. Toirmisctear aon athbhreithniú, atarchur nó leathadh a dhéanamh ar an bhfaisnéis seo, aon úsáid eile a bhaint aisti nó aon ghníomh a dhéanamh ar a hiontaoibh, ag daoine nó ag eintitis seachas an faighteoir beartaithe. Má fuair tú é seo trí dhearmad, téigh i dteagmháil leis an seoltóir, le do thoil, agus scrios an t-ábhar as aon ríomhaire. Is é beartas na Roinne Dlí agus Cirt, Comhionannais agus Athchóirithe Dlí, agus na nOifígí agus na nGníomhaireachtaí a úsáideann seirbhísí TF na Roinne, seoladh ábhair cholúil a dhícheadú. Más rud é go measann tú gur ábhar colúil atá san ábhar atá sa teachtaireacht seo is ceart duit dul i dteagmháil leis an seoltóir láithreach agus le mailminder[ag]justice.ie chomh maith. *********************************************************************************** ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: Estimating Missing Dependent Variables
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Gerard,
The form of the assumed distribution of probabilities (normal or logistic or whatever) is irrelevant to the point I am making. In the case of a dichotomous variable treated with log reg, you do not "fit a logistic distribution" to the distribution of subjects over the two values of the variable: the two values remain two values, people sit only at the two values with nobody in between, and the log distribution pertains to the probability of one of the values in a group of people, which varies from group to group as other variable(s) vary. In the case of a continuous variable, the normal distribution is not required for the dependent variable itself: linear regression only assumes that the errors (the "e" in the equation) are normally distributed around the regression line, which is not quite the same. You do not "fit a normal distribution" to the distribution of subjects over the dependent variable in a linear regression. And moreover, all of this has nothing to do with my point. Probably the difficulty in "seeing" my point is that many of us have been for long considering probabilities as attributes of the individuals. Often we see variables, dichotomous or interval, as arguments of an underlying probability distribution whereby each value of the variable and the individual cases having that value are assigned a probability. So one imagines the logistic distribution as representing a low (or zero) probability for individuals not suffering the event, a high (or unit) probability for individuals having the event, and intermediate probabilities for the fictitious individuals in between. But this is all imaginary, and a bit quaint, because there are no intermediate situations, and there is no objective or empirical "probability" property in individuals. It is, at best, a construct you assign to individuals after measuring it in groups. If you adopt a frequentist view of probability, which is the one with better mathematical foundations and sounder empirical basis, things become easier and interpretations more natural. Hector -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Gerard M. Keogh Sent: 11 June 2009 06:29 To: [hidden email] Subject: Re: Estimating Missing Dependent Variables Hector, I think thing are not as clear cut as you say. In a logistic model the probabilities come from a logistic distribution - forget about error it only confuses things. Estimation involves fitting a logistic distribution to get estimated probabilities. Similarly in a normal model the data values themselves are normally distributed and estimation involves fitting a normal dist to the y values. For bernoulli data as you describe the key thing is that logit transforms the [0,1] probability scale [-inf, +inf]. For normal data this transformation is the identity. Gerard Hector Maletta <hmaletta@fiberte l.com.ar> To Sent by: [hidden email] "SPSSX(r) cc Discussion" <SPSSX-L@LISTSERV Subject .UGA.EDU> Re: Estimating Missing Dependent Variables 10/06/2009 19:28 Please respond to Hector Maletta <hmaletta@fiberte l.com.ar> Last comments indeed. In all statistical estimates there is a margin of error, granted, Jon. But in regression you actually estimate the value, and your THEORETICAL model includes the error: y=a+bX+e. The actual event is SUPPOSED to obey two kinds of causes, one systematic (X) and one random (e). Thus you obtain and estimate of the expected value (a+bX) and an estimate of the error component (e); the least squares algorithm chooses a and b such that the sum of the squared error components e is minimized. Instead in logistic regression your theoretical model for an individual is totally different. It is deterministic. Either she is in State A or State B. No middle way. Either she drops out of college or she doesnt. Either she is alive or she is dead. There is no probability or error in the model for individuals, only the two stark discrete states. What you predict, what you deal about indeed, is not the state of each individual, but the probability (read: EXPECTED RELATIVE FREQUENCY) of one of the states IN A GROUP OF INDIVIDUALS. Your margin of error would be in this relative frequency: for instance when you throw 100 coins, the expected frequency of tails is 50, but perhaps you get 49 or 52, and that is your margin of error. By the same token, if your model predicts (for some group sharing certain combination of predictors values) a probability of 0.20, perhaps the proportion of actual events turns out to be 0.22 or 0.18. The error is in the prediction of the relative frequency, not in the estimation of each individual outcome, because you are not predicting individual outcomes in that kind of models. Hector From: Peck, Jon [mailto:[hidden email]] Sent: 10 June 2009 13:55 To: Hector Maletta; [hidden email] Subject: RE: Re: [SPSSX-L] Estimating Missing Dependent Variables A few more last comments below. From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Hector Maletta Sent: Monday, June 08, 2009 9:46 PM To: [hidden email] Subject: Re: [SPSSX-L] Estimating Missing Dependent Variables Moreover, Jon, Besides the decision question being different from the question of meaning and estimation of the probability, in any case your decision will affect entire groups or categories of people; you would be unable to say anything about how the die will roll in each particular case within each category of people sharing the same probability. Some people with high probability will not suffer the event, while some with very low probability will. [>>>Peck, Jon] And in the same way, in an ordinary conditional expectation model, some units will have higher than expected outcomes and some lower, and a regression equation cannot say any more about which are which given equal expectation. You, for instance, may decide to give a college scholarship (or student loan) to all candidates whose predicted probability of college success is over 0.8. Some of them will actually succeed, some will not, and you do not have a clue about which is which. By the same token, you as a doctor should decide on giving or not giving Treatment A to patients suffering certain painful disease which (if untreated) would probably kill them in a few years. The treatment is effective in most cases, but in some cases it has lethal side effects that would kill the patient instantly; that unfortunate outcome is never certain: its probability p depends on some predictors. You (or the medical profession) give the treatment to all patients whose p is lower than, say, 1%. But you do not know in advance whether your next patient (estimated p=0.009) will be cured, or she is instead a member of the unlucky lot that will be instantly killed by the treatment. Its kinda Russian roulette at that point, only the gun has 100 holes, of which 99 are empty and one has a bullet. Knowing the probability of a category of people tells you nothing about the individual fate of each patient, just as (in Russian roulette) knowing that you have 1 chance in 6 tells you nothing how things will turn out the next time you pull the trigger. [>>>Peck, Jon] Isn't it equivalent to say that a very good p function in the extreme predicting 0 or 1 probabilities, is like a regression equation with a very high fit/small error? If there is inherent randomness, no model is going to capture that (but some vigorous overfitting might make it seem otherwise L) Hector **************************************************************************** ****** The information transmitted is intended only for the person or entity to which it is addressed and may contain confidential and/or privileged material. Any review, retransmission, dissemination or other use of, or taking of any action in reliance upon, this information by persons or entities other than the intended recipient is prohibited. If you received this in error, please contact the sender and delete the material from any computer. It is the policy of the Department of Justice, Equality and Law Reform and the Agencies and Offices using its IT services to disallow the sending of offensive material. Should you consider that the material contained in this message is offensive you should contact the sender immediately and also mailminder[at]justice.ie. Is le haghaidh an duine nó an eintitis ar a bhfuil sí dírithe, agus le haghaidh an duine nó an eintitis sin amháin, a bheartaítear an fhaisnéis a tarchuireadh agus féadfaidh sé go bhfuil ábhar faoi rún agus/nó faoi phribhléid inti. Toirmisctear aon athbhreithniú, atarchur nó leathadh a dhéanamh ar an bhfaisnéis seo, aon úsáid eile a bhaint aisti nó aon ghníomh a dhéanamh ar a hiontaoibh, ag daoine nó ag eintitis seachas an faighteoir beartaithe. Má fuair tú é seo trí dhearmad, téigh i dteagmháil leis an seoltóir, le do thoil, agus scrios an t-ábhar as aon ríomhaire. Is é beartas na Roinne Dlí agus Cirt, Comhionannais agus Athchóirithe Dlí, agus na nOifígí agus na nGníomhaireachtaí a úsáideann seirbhísí TF na Roinne, seoladh ábhair cholúil a dhícheadú. Más rud é go measann tú gur ábhar colúil atá san ábhar atá sa teachtaireacht seo is ceart duit dul i dteagmháil leis an seoltóir láithreach agus le mailminder[ag]justice.ie chomh maith. **************************************************************************** ******* ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: Estimating Missing Dependent Variables
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The mechanics is as you say. I am talking about the substantive meaning of
the operation. On second thought, I correct a previous statement I made: also in the case of linear regression what you actually predict is the EXPECTED value of a GROUP of people sharing certain value(s) of predictor variable(s), i.e. the average value of Y for that group of people. Individuals are distributed around the expected value, and may have any value of Y, with a presumed normal distribution around the expected value, and you do not have a clue about where a particular individual will be. That is, also in this case the prediction is about a group, not about individuals. What you are saying in a linear regression is more or less like this: "If you take a certain number of women of age 40 with 12 years of education and and income of $35,000 their expected average net wealth is $52,000". As a subsidiary prediction you are also saying that "The actual net wealths of the various women in the group are normally distributed around a mean of $52,000 and a SD=SE, where SE is also estimated by the regression model". Given a particular woman, Ms Smith, with the given characteristics, you cannot say anything else about how much is her net wealth. However, in linear regression you partition the entire sample in many subgroups (ultimately as many as cases, if individual values are not repeated) and predict a value of Y for each combination of predictor values, and separately you predict a probability distribution of cases in the subgroup around the predicted value of the variable. In a logistic regression, instead, if you take a group of 100 women with the same characteristics of the previous example, you may predict that about 43 of them are currently married, and the remaining 57 unmarried; for another group of women with different characteristics, you predict that 77 will be married. But you do not predict the marital status of Ms Smith, a member of the first group, or Ms Jones, a member of the second group, nor the distribution of the members around the "predicted value" because you do not predict any "value". About the practical implications of thinking probabilities in frequentist or non frequentist terms, you may like to see Gerd Gigerenzer (2000), Adaptive Thinking: Rationality in the Real World, OUP (e.g. pp.17-19 and elsewhere). Hector -----Original Message----- From: Gerard M. Keogh [mailto:[hidden email]] Sent: 11 June 2009 10:49 To: Hector Maletta Subject: Re: Estimating Missing Dependent Variables Hector, I'm not hung up on this! .... You do not "fit a normal distribution" to the distribution of subjects over the dependent variable in a linear regression.... I fit a normal dist to the dependent var for each subj conditional on the indep vars - E[y|x]. This is just integration which marginalises out the y variable giving y_bar = mu(x). It's just a mechanical process with no hidden meaning. For the logistic we use g(E[y|x]) where g is the link function or logit. And yes, it's a construct but no different to the normal data case where g = identity - no different because it's all just integration of weighted pdf's. food for thought though! Gerard Hector Maletta <hmaletta@fiberte l.com.ar> To Sent by: [hidden email] "SPSSX(r) cc Discussion" <SPSSX-L@LISTSERV Subject .UGA.EDU> Re: Estimating Missing Dependent Variables 11/06/2009 14:20 Please respond to Hector Maletta <hmaletta@fiberte l.com.ar> Gerard, The form of the assumed distribution of probabilities (normal or logistic or whatever) is irrelevant to the point I am making. In the case of a dichotomous variable treated with log reg, you do not "fit a logistic distribution" to the distribution of subjects over the two values of the variable: the two values remain two values, people sit only at the two values with nobody in between, and the log distribution pertains to the probability of one of the values in a group of people, which varies from group to group as other variable(s) vary. In the case of a continuous variable, the normal distribution is not required for the dependent variable itself: linear regression only assumes that the errors (the "e" in the equation) are normally distributed around the regression line, which is not quite the same. You do not "fit a normal distribution" to the distribution of subjects over the dependent variable in a linear regression. And moreover, all of this has nothing to do with my point. Probably the difficulty in "seeing" my point is that many of us have been for long considering probabilities as attributes of the individuals. Often we see variables, dichotomous or interval, as arguments of an underlying probability distribution whereby each value of the variable and the individual cases having that value are assigned a probability. So one imagines the logistic distribution as representing a low (or zero) probability for individuals not suffering the event, a high (or unit) probability for individuals having the event, and intermediate probabilities for the fictitious individuals in between. But this is all imaginary, and a bit quaint, because there are no intermediate situations, and there is no objective or empirical "probability" property in individuals. It is, at best, a construct you assign to individuals after measuring it in groups. If you adopt a frequentist view of probability, which is the one with better mathematical foundations and sounder empirical basis, things become easier and interpretations more natural. Hector -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Gerard M. Keogh Sent: 11 June 2009 06:29 To: [hidden email] Subject: Re: Estimating Missing Dependent Variables Hector, I think thing are not as clear cut as you say. In a logistic model the probabilities come from a logistic distribution - forget about error it only confuses things. Estimation involves fitting a logistic distribution to get estimated probabilities. Similarly in a normal model the data values themselves are normally distributed and estimation involves fitting a normal dist to the y values. For bernoulli data as you describe the key thing is that logit transforms the [0,1] probability scale [-inf, +inf]. For normal data this transformation is the identity. Gerard Hector Maletta <hmaletta@fiberte l.com.ar> To Sent by: [hidden email] "SPSSX(r) cc Discussion" <SPSSX-L@LISTSERV Subject .UGA.EDU> Re: Estimating Missing Dependent Variables 10/06/2009 19:28 Please respond to Hector Maletta <hmaletta@fiberte l.com.ar> Last comments indeed. In all statistical estimates there is a margin of error, granted, Jon. But in regression you actually estimate the value, and your THEORETICAL model includes the error: y=a+bX+e. The actual event is SUPPOSED to obey two kinds of causes, one systematic (X) and one random (e). Thus you obtain and estimate of the expected value (a+bX) and an estimate of the error component (e); the least squares algorithm chooses a and b such that the sum of the squared error components e is minimized. Instead in logistic regression your theoretical model for an individual is totally different. It is deterministic. Either she is in State A or State B. No middle way. Either she drops out of college or she doesnt. Either she is alive or she is dead. There is no probability or error in the model for individuals, only the two stark discrete states. What you predict, what you deal about indeed, is not the state of each individual, but the probability (read: EXPECTED RELATIVE FREQUENCY) of one of the states IN A GROUP OF INDIVIDUALS. Your margin of error would be in this relative frequency: for instance when you throw 100 coins, the expected frequency of tails is 50, but perhaps you get 49 or 52, and that is your margin of error. By the same token, if your model predicts (for some group sharing certain combination of predictors values) a probability of 0.20, perhaps the proportion of actual events turns out to be 0.22 or 0.18. The error is in the prediction of the relative frequency, not in the estimation of each individual outcome, because you are not predicting individual outcomes in that kind of models. Hector From: Peck, Jon [mailto:[hidden email]] Sent: 10 June 2009 13:55 To: Hector Maletta; [hidden email] Subject: RE: Re: [SPSSX-L] Estimating Missing Dependent Variables A few more last comments below. From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Hector Maletta Sent: Monday, June 08, 2009 9:46 PM To: [hidden email] Subject: Re: [SPSSX-L] Estimating Missing Dependent Variables Moreover, Jon, Besides the decision question being different from the question of meaning and estimation of the probability, in any case your decision will affect entire groups or categories of people; you would be unable to say anything about how the die will roll in each particular case within each category of people sharing the same probability. Some people with high probability will not suffer the event, while some with very low probability will. [>>>Peck, Jon] And in the same way, in an ordinary conditional expectation model, some units will have higher than expected outcomes and some lower, and a regression equation cannot say any more about which are which given equal expectation. You, for instance, may decide to give a college scholarship (or student loan) to all candidates whose predicted probability of college success is over 0.8. Some of them will actually succeed, some will not, and you do not have a clue about which is which. By the same token, you as a doctor should decide on giving or not giving Treatment A to patients suffering certain painful disease which (if untreated) would probably kill them in a few years. The treatment is effective in most cases, but in some cases it has lethal side effects that would kill the patient instantly; that unfortunate outcome is never certain: its probability p depends on some predictors. You (or the medical profession) give the treatment to all patients whose p is lower than, say, 1%. But you do not know in advance whether your next patient (estimated p=0.009) will be cured, or she is instead a member of the unlucky lot that will be instantly killed by the treatment. Its kinda Russian roulette at that point, only the gun has 100 holes, of which 99 are empty and one has a bullet. Knowing the probability of a category of people tells you nothing about the individual fate of each patient, just as (in Russian roulette) knowing that you have 1 chance in 6 tells you nothing how things will turn out the next time you pull the trigger. [>>>Peck, Jon] Isn't it equivalent to say that a very good p function in the extreme predicting 0 or 1 probabilities, is like a regression equation with a very high fit/small error? If there is inherent randomness, no model is going to capture that (but some vigorous overfitting might make it seem otherwise L) Hector **************************************************************************** ****** The information transmitted is intended only for the person or entity to which it is addressed and may contain confidential and/or privileged material. Any review, retransmission, dissemination or other use of, or taking of any action in reliance upon, this information by persons or entities other than the intended recipient is prohibited. If you received this in error, please contact the sender and delete the material from any computer. It is the policy of the Department of Justice, Equality and Law Reform and the Agencies and Offices using its IT services to disallow the sending of offensive material. Should you consider that the material contained in this message is offensive you should contact the sender immediately and also mailminder[at]justice.ie. Is le haghaidh an duine nó an eintitis ar a bhfuil sí dírithe, agus le haghaidh an duine nó an eintitis sin amháin, a bheartaítear an fhaisnéis a tarchuireadh agus féadfaidh sé go bhfuil ábhar faoi rún agus/nó faoi phribhléid inti. Toirmisctear aon athbhreithniú, atarchur nó leathadh a dhéanamh ar an bhfaisnéis seo, aon úsáid eile a bhaint aisti nó aon ghníomh a dhéanamh ar a hiontaoibh, ag daoine nó ag eintitis seachas an faighteoir beartaithe. Má fuair tú é seo trí dhearmad, téigh i dteagmháil leis an seoltóir, le do thoil, agus scrios an t-ábhar as aon ríomhaire. Is é beartas na Roinne Dlí agus Cirt, Comhionannais agus Athchóirithe Dlí, agus na nOifígí agus na nGníomhaireachtaí a úsáideann seirbhísí TF na Roinne, seoladh ábhair cholúil a dhícheadú. Más rud é go measann tú gur ábhar colúil atá san ábhar atá sa teachtaireacht seo is ceart duit dul i dteagmháil leis an seoltóir láithreach agus le mailminder[ag]justice.ie chomh maith. **************************************************************************** ******* ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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