**Transcript of Cyberseminar**

**HERC Econometrics with Observational Data**

**Non-linear Dependent Variables**

**Presenter: Ciaran S. Phibbs**

**May 30, 2012**

Ciaran S. Phibbs:Good Morning or Good Afternoon, depending on your time zone. In making this slide, I note that the title is slightly different, Nonlinear versus Limited. That is because nonlinear is actually a broader class of variables. I am going to focus on limited dependent variables. Examples of limited dependent variables are situations where you have a 0-1 or a yes, no dependent variable, or a small number of options or you are dealing with actual integer counts, but they are small. The common theme of all of these is not only is the dependent variable not continuous, it is not even close to continuous, and for some of the things it has restrictions. For example, with counts you do not have negatives. And all of these pose problems for OLS.

A brief outline of the things that I am going to specifically cover is I am going to talk about Binary Choices, or yes, nos. I am going to talk about a Multinomial Choice. That is where there is more than one choice, and I am going to talk about modeling Counts. The models are in the general framework of a probability of an event occurring. The probability of that could be the probability that one chooses an option, or that a count occurs.

In very simplistic terms, these models have problems with heteroscedastic error terms, and with predictions that are not constrained to match actual outcomes in terms of applying the general OLS model. And there is a very real problem with predicted values being negative when a negative number isn’t possible.

And to introduce this in a general term for something one doesn’t consider, if one considers the classical OLS model listed up here where you have and independent variable Y, as a function of an intercept, and a set of dependent variables, Beta X, and your error term E. Let’s consider the simple yes, no, or mortality where Y takes 0 if you lived, and 1 if the patient died. In terms of prediction, that is formally expressed that the probability of Y=1 is equal to some function of X, Beta, and the probability of Y=1 is one minus that F of X data. If one were to estimate this with a standard OLS model in what people also call a linear probability model, there are serious problems; most explicitly your error term EI is heteroscedastic because it depends directly on the Beta’s or the X’s. It is also the case that for OLS the predictions are not constrained to be exactly 0 or exactly 1, which is the only two possible outcomes. More importantly you can get predictions that go outside of the sample, and it can cause problems when one tries to generate predicting values. If OLS has a hard time estimating these if you have very low mortality rates for example, you can get some estimates where the parameter estimates really don’t make sense, in addition to all of the other underlying problems. 

So in terms of thinking about this I have given one example here. Compared to other things, we don’t have the white board function that we have anymore. I am going to ask a question in order to start people thinking about it. But what you can do is you can answer this in your question screen. What are some other examples of binary outcomes that are common problems in health care that we might use this format of a model for. You can just enter them in your questions, and Heidi and Jean will read them out.  Are answers showing up?

Heidi or Jean:No. Not yet. To get to your Q&A it’s on the dashboard on the right hand side of your screen. It says Collapse. Just click on that orange arrow and it will open that back up for you. Somebody said whether or not someone has a mental health condition?

Ciaran S. Phibbs:Okay, so the probability of a condition occurring.

Heidi or Jean:Somebody else wrote Admissions.

Ciaran S. Phibbs:Okay. 

Heidi or Jean:Did or did not get treatments.

Ciaran S. Phibbs:Okay.

Heidi or Jean:Died, yes or no. Infection, yes or no. Somebody else said disabled or not. Insurance, yes or no. Rehospitalization, Rare Events, Suicide. 

Ciaran S. Phibbs:Okay. I am going to actually move on. We are interested in binary outcomes an awful lot in health care applications. Mortality, morbidity, infection, a patient safety event, decisions to seek medical care. A lot of these were alluded to in the conditions, but an awful lot of our health care applications really are binary. 

The standard approach that is very common in health care is what is called the logistic regression. What that is formulary modeling is the probability that Y=1 is defined as the exponent of the X, Beta, divided by 1 + the exponent of the X, Beta. That is the logit function. 

There are a couple of things to note with logistic regression. It is designed for relatively rare events; so logistic is not a good choice if you are modeling something where it is a 50/50 proposition. And I will talk a little bit more about that later in terms of interpreting the results. The other advantage of a logistic is that it is commonly used in health care. And because it is so commonly used, a lot of readers of medical journals are used to the idea of odds ratios and can interpret them and sort of know what they mean. 

Another approach, which is more common in economics, is a probit regression. A classic example of a probit regression is actually the decision to make a large purchase. It is a little bit different functional form where you are modeling y* = Beta, X + error term and where y=1 or you made the purchase or the decision and y* is greater than 0 and in 0 if y* is less than 0. 

I will note that there are some other methods using other distributions. A couple of things to note is in general logistic and probit give about the same answer once you sort through the differences and how you actually directly interpret them. But, remember you are manipulating the same X, Beta matrix. So it is not surprising they give fairly similar answers. There are different distributions underlying it so you get slightly different answers, but they tend to be fairly similar. In terms of what economists call the marginal effects, that used to be easier to directly generate those out of probit in terms of standardized packages. But, that is not so any more. This data will do just about anything.

Most people are familiar with the logistic, and that is the one commonly used. Because most people are mentioning one versus the other, I would like to note that there is something that one needs to be aware in terms of the odds ratios and the relative risks. One looks at an odds ratio, the standard method of interpreting a logistic regression is the odds ratio and then directly converting that to a % effect, which is really a relative risk. What I mean is you get an odds ratio of 1.5 that is interpreted as a 50% increase in the risk of, or the probability of that event occurring, which is a relative risk. And that is not fully correct. What you are doing is that it is a 50% chance in the law of odds, and the other thing that is very important to realize is that this direct % effect is an approximation. This approximation starts to break down when outcome of interest hits 10%. Remember I noted earlier that the logistic is designed for relatively rare events, and this is all from the JAMA paper in terms of interpreting the difference between an odds ratio and a risk ratio. So at 1 it is linear, and the bottom of this graph shows the title as Incidence Among the Nonexposed. If we were modeling mortality, think of this as the mortality rate in the sample population. Here is your odds ratio and you can see at very close numbers, this line is almost straight. It starts to deviate around from being straight more or bigger numbers. So even at 5% mortality rate if your odds ratio is 3, that is already starting to pull away from the 3 in terms of going up. At the risk ratio if you go up to 40%, you can see can see these curves are bending up quite steeply. 

There is a way to address this that is an approximately calculation. It is not perfect, but it is pretty close. This shows the reference in JAMA for converting the odds ratio into a relative risk where in simple form you take your odds ratio and you are adjusting it by the sample probability of the outcome of interest in this example I have been using through here. We are talking about mortality. And just to show you the impact of this, this is from a paper that I did a few years ago in the *New England Journal* where we used logistic to model mortality, but in a sample where the mortality was about 20%. As you can see down here with an odds ratio of 1.08, the relative risk is almost the same 1.06. At 1.5 it drops by about 20% to 1.38. And those numbers get bigger up here when I had a 2.72 odds ratio is only a 2.08 relative risk. And I just want to emphasize that one needs to remember this when presenting the results of ones analysis.

For logistic models and probit and even some of the other models, the standard statistical packages will now handle a wide range of things you can estimate. A couple of years ago with the Stata account I did, there were 34 different related estimation commands for limited dependent variables. Given that that is from a couple versions of Stata ago, I am sure that that is now larger. This is for binary choice options. You can now estimate panel data using both random and fixed effects. There are various things for different types of grouping data. The point is that it is not just, “Oh, I’m going to run a logistic regression.” The methods vary for different types of data as well, be it a panel, which is repeated observations of the same cross section. For grouped data or for time series data, there are all these different types of data structures and estimation commands. Just as within OLS, you have different estimation commands and different assumptions that need to be dealt with.  When you are dealing with different types of data, you need to be aware of that with different types in terms in the structure of the data when you have a 0-1 dependent variable.

The other thing I want to talk about is goodness of fit tests. The most commonly reported statistics are the area under the ROC curve. If you are using SAS, that shows up in logistic and c-statistic. An area under the ROC or Receiver Operator Curve, has a range of 0.50 to 1.0, where 0.50 represents essentially flipping a coin. It is chance in terms of whether you are correctly assigning each observation to the right group based on the model, and an ROC of 1.0 means that your model is perfectly predicting the outcomes of every observation. It is a continuum. The other commonly used test is the Hosmer-Lemeshow test, which I am going to talk about in a minute for that same *New England Journal*paper. I put predictions up there. These things tend to move in concert, so if you want to reject, for the Hosmer-Lemeshow test, you want a big P value. You want to be able to reject, and that tends to be correlated. You will more likely reject if you have a very good c-statistic. For this paper I had a c-statistic of 0.86, which for most applications is a very good c-statistic. The Hosmer-Lemeshow test was rejected and it was not close. 

What the Hosmer-Lemeshow test does is that it breaks the sample into N groups. It is usually 10. That is what Hosmer-Lemeshow introduced in their original article. Stata will actually let you vary the number of groups if you so desire based on the size of your sample. And it breaks the sample into 10 equal groups.  They are ranked ordered by the probability of the event according to the model, and it compares the number of observed and expected events in each group. One thing to note is that you are trying to predict mortality. If your model predicts well, the events will be concentrated in the one or two of the highest risk groups. There may be times when you want to look a little more carefully at how well you are predicting. So what you can do is to sort this sample differently. It is not a formal test, but it is a good check to see how instead of dividing into equal numbers of groups, you can make it so that you have equal numbers of predicted deaths in these groups and then compare. That gives you a little bit more discrimination in terms of how you really are predicting among the subset of patients that are really high risk. It may be a useful thing to do if you are really concerned about how you are predicting, and it is only a very small subset.

A note about estimated these models. Because these are maximum likelihood models, it takes a lot more computer resources to do it. If you have really big samples, millions, it will take a lot longer to estimate a maximum likelihood model than and OLS model. If you don’t have a super big computer but you still want to use the large sample, there is a way around this. The X matrix is exactly the same in OLS, and the P values are virtually the same for an OLS model as for the logit model. If you estimate the model in OLS, it will estimate much faster. You can look and see what the P values are, and you can see the magnitude and relative size of the coefficients, but they aren’t meaningful in terms of trying to interpret them. To speed the running of your regression if you are constrained in terms of computer power, you can do your model development using OLS and then just estimate your final models with logit or the other maximum likelihood model so that you can get the correct parameter estimates. So this is a way to get around restrictions on computing power and time. If you want to play around with the model in terms of model bit, or you are trying to work on this functional form of variables and some of that kind of thing, using OLS as an alternative if you are constrained in terms of computing power maybe, you can alter it.

I now want to move to what is called a Multinomial Choice. You can think of a multinomial choice as more than one outcome. The estimation options are more limited. There is a multivariable probit model, which is the idea that you have multiple decisions, each of which there are two alternatives. And then there are two different ways of using a logit model where it is a single decision and multiple alternatives. So which one you go to depends on what the underlying decision structure is. I am actually going to talk about the different logit models. 

The two choices for the logit model for multiple choices are the conditional logit model, which is associated with Dan McFadden. This is for unordered choices. And then there is a multinomial logit model. For this the choices can be ordered, but it is not required. They each have advantages and disadvantages in terms of the model.

Turning to examples of what we might want to use this for and that both models have been applied to is a choice of what hospital to use among those in the market. Patients have choices. This could also be extended to other types of providers in terms of where does the patient go when you are observing that choice. And that is somewhat consistent to the way the original McFadden model was derived, which was looking at the individuals choice of what mode of transportation to use to get to work. Other options could be a choice of treatment among several options. As an example, I am sure many of you can come up with other examples. There are lots of cases where we are trying to look at what was chosen among several options.

With the Conditional Logit Model you have j choices. And the probability that individual i chooses j is a function of the exponent of the Beta, Xs or ij. This is divided by the sum for all of the possible choices of that exponent. So it the probability for that one divided by the sum of all of them. This conditional logit model is also known as the random utility model. It is directly derived from consumer theory. For those of you writing grant proposals where you are looking at choices, and they always want to know your theoretical framework. Some reviewers are really picky about that. This gives you directly derived consumer theory, and you can refer to the fact that Dan McFadden won a Nobel Prize for this. 

Looking at how consumers choose from a set of options, the model is driven by the characteristics of the choices. Individual characteristics “cancel out” in the model. But they can be included indirectly. Also some of those characteristics of the choice can vary by person. And let’s just go back to this hospital choice example. You know where an individual lives. So a characteristic as a choice is how long does it take the patient to get from their home to the hospital that can be a straight-line distance driving time? So they can vary and that’s okay, because that’s then a characteristic of the choice and not of the individual. But you can’t include individual characteristics. They “cancel out,” because they will be the same for all the individuals. But there is a way to get that into the back door if you can interact in this example an individual characteristic with a choice specific characteristic that varies across choices. So you could interact, “Is the patient a Medicaid patient with distance to the hospital?” Or you could interact, “Is the patient a Medicaid with the share of the patients at that hospital that are Medicaid patients. There is this observation that Medicaid patients are more likely to go to a hospital that has a lot of Medicaid patients. So it is a way of getting those types of individual characteristics back into a model that doesn’t specifically, but it has to be with that interaction with something like distance and is a choice specific variable that is continuous. Another advantage of the McFadden Model is that results can be easily expressed as odds ratios.

I want to talk about a couple of notes about the software packages. Unless they have changed it in SAS, it used to be really Clogit to estimate these models in SAS, because it essentially required that the number of choices be equal across all observations. LIMDEP was an economic developed package specifically designed for limited dependent variables. In their estimation of this model, there is a “NCHOICES” option that let’s you set the number of choices for each observation. I haven’t fully explored it, but someone has told me that in Stata Clogit program, which is the conditional logit program, you can do this with a group option. What this does for example is that if you are again looking at the choice of hospitals, you can limit the hospitals to the hospitals that patients in a given zip code might feasibly choose in terms of options that are a part of the market. And that will vary depending on where the patient lives. This allows you to get the examples. So having for a large number of applications the ability to vary the number of choices based on who’s choosing may be a very useful feature. It is not necessarily true if you were looking at something like a treatment choice. A treatment choice is something where you might want to have more individual characteristics. So the conditional logit model may not be the appropriate choice.

Just to give you some number because I had them handy, was an estimate I pulled up of a study that I did years ago where we were looking at given where a veteran lived, their choice of a VA or a non-VA hospital. And you can see that the probability of choosing any hospital went down as the distance to that hospital went up. But the probably that a veteran was to choose the hospital was much higher than it was at the VA hospital, holding distance costs.

The Multinomial Logit Model is a little bit different in that you have to have a reference choice. You are looking at the probability of choosing this top expression is fairly similar to what is in the conditional logit. That is for choosing yes, but it is also 1 divided by the same denominator if they don’t choose it. In terms of the multinomial logit model, the key factor is that essentially you have to generate a reference choice, and that the model yields a set of estimates for each of the other choices relative to the reference choice.

The advantage of how this is structured is that it allows you to include direct estimation of individual characteristics in the model. The model can and really should include parameters or variables for the choice characteristics as well. But it allows you to directly estimate in a much more robust way to include individual characteristics. I referred earlier to when I was looking at a treatment choice. So let’s say that we are modeling a decision, and I will just arbitrarily pick a condition for which there are three treatments. You could look at management of angina where there is medical management, or you could use angioplasty or you could do coronary artery bypass. Those are two different forms of surgery. Those are the three options for managing that condition. What we have to do in terms of modeling that is one would have to include a reference. So we could say we are going to make medical management be the reference group, and then we are going to look and then we get a set of estimates for angioplasty compared to medical management and for Cavage compared to medical management. So in interpreting them and presenting them, one has to be very careful about how one presents the results. And make sure that you couch it in terms of these relative terms. But for that type of a choice, individual characteristics could well be very important. For example, the type of choice makes could very well vary by age, and one needs to include those.

The important thing for both of these models is something called the Independence of Irrelevant Alternatives. And that is that the results should be robust to varying the alternative choices. There are a couple of ways to see if it really works. One is to re-estimate the model after deleting some of the choices, and seeing if your parameter estimates especially on the variables of interest are relatively robust. McFadden did develop a regression based test for the multinomial logit model. The reference is listed here. It is fairly easy to do. It is based on estimating the model, getting the residuals, and running another regression. One of the things that is frequently the case is you really have choices where you will fail the IIA assumption, is if you have a set that is really a nested model where people are making two choices, and that you need to estimate a series of models.

There are a couple of notes about the Independence of Irrelevant Alternatives is that that McFadden test that I referred to can also be used to test for omitted variables. It is outlined in the paper. And for many health applications, I will note that it really doesn’t matter. For models of hospital choice, they are very robust, and that is because hospital choice is really strongly driven by distance. So if you omit a few of alternatives, you get a very similar result.

I am going to move onto Count Data, which are integers. This is a continuation of the same underlying program where the dependent variable can only assume specific values and can’t be less than zero. The problems in terms of estimating with other alternative models versus ordinary squares, diminishes the counts increase. The rule of thumb is that if you are looking at integers and all the counts are under 30, you should be using a count data model. The rule of thumb is fuzzy as to when you switch as you get more numbers. So I have data where I am looking at some sort of a count, let’s say number of outpatient visits, some people may have more than 30. But most people are having 0, 1, 2, 3; I would probably still estimate that with a count.

I have mentioned one example, but I am going to go to the white board again just to start you thinking about things that are counts that we might be interested in, where we are going to have a lot of small integers, and you can go to the questions. Are people answering?

Heidi or Jean:Not yet.

Ciaran S. Phibbs:Remember, you can go to your orange arrow on the help box. Open up the questions and type in an answer of some examples of health applications where we might where our dependent variables really are counts.

Heidi or Jean:You have someone who said “falls.”

Ciaran S. Phibbs:Okay, if a patient falls is some indication, but also problematic in nursing homes.

Heidi or Jean:Somebody else said number of bloodstream infections per month.

Ciaran S. Phibbs:Okay, so we would be looking at either a unit or a hospital and the number of rare events where you are just going to count them. That is true. 

Heidi or Jean:Somebody else said number of inpatient admissions.

Ciaran S. Phibbs:Yes, having a number of inpatient admissions would give small counts. The number of admissions that a patient had in a year would be a small count for most people. 

Heidi or Jean:Some people also said utilization of services, number of readmissions.

Ciaran S. Phibbs:Yeah, number of readmissions depending on the denominator, utilization of services. I mentioned outpatient visits. Most people don’t use that many. The number of times the patient refills a prescription, and the number of adverse events in a unit or a hospital. You have hit on the examples that I put up here, but there are actually a lot of things that we might be interested in that are rare events, and if we have them as a count. One of the things that I will note in terms using a count data model is that the count data model really is the right data to generating structure, because you are looking at a count of an event. And converting them to a rate and running OLS can be very problematic. And the reason that it is problematic is that OLS really doesn’t work well when you have the preponderance of your observations having zeros. 

The classic Count Data model is the Poisson distribution. Most people in the introductory statistics class get a Poisson for looking at counts. I have written the formula here. It is a complex combination exponent of lambda times lambda times the i divided by the y exponentiated. One of the things that underlie this as a problem is that it has a very restrictive assumption that the mean and the variance are equal. 

The negative binomial is often a better choice in Stata, because it allows for more dispersion. It allows the standard deviation to be bigger than the mean, which is frequently the case. I am not going to go through all of the math here. I have written out the distribution. It is slightly different. One thing to note is that in Stata, the relative command is nbreg for negative binomial. And if you are using Stata nbreg automatically runs the model in both Stata and using the negative binomial distribution, and generates a test of what they call over dispersion that tells you which model you should use. There is also a generalized version of this, which allows even more flexibility in terms of what distribution you use. If the negative binomial distribution doesn’t exactly fit the data, there are ways to manipulate it to get a better fit. The results are somewhat similar if you estimate in health applications where the standard deviation is much greater than the variance, you can still estimate with a _____ [00:40:25]. The answer is all that different but as the variance gets bigger, it will deviate more. 

In terms of interpreting the count model, and they both have the same interpretation, is that you have a log of the event rate is equal to Beta, X. And so what is called the Incidence Rate Ratio is the exponent of Beta. It’s like an odds ratio with a similar interpretation. So in terms of this, this is just a number that I pulled from a regression I ran where I am looking at the effect of average amount of time that the RN has been working on the unit, on the infection rate. And as that goes up by a year is the unit of observation. So the Beta of –0.262 gives you an instant incidence rate ratio of 0.770, or a 23% reduction in infection rate. It may be a little bit unrealistic, but I am just trying to put some parameters out there for you to interpret in terms of what you are seeing and how to interpret them.

In terms of this I want to note that when one looks in the literature, it is more common compared to say a logistic, to see OLS used for counts compared to things where it is a yes, no. I looked at this a minute ago; there is a real problem with using OLS when there are lots of zeros, because OLS just can’t handle it. Not only are the predicted values off, but also the estimated values can get fairly strange. And more importantly, when you are looking at rare events with all of these zeros, OLS doesn’t happen. It actually reduces, and sometimes by an awful lot, the statistical significance of your results. As a result if you have counts, you really need to consider using one of these models. 

Another thing to note is that for count data models is that 30 is a rule of thumb, but you should still consider a count data model if most of the counts are small. I alluded earlier to the example of looking at the number of outpatient visits. And there are some people that are going to be in the sample with intensive medical needs where there is a moderate number of people who have more than 30 visits a year. We certainly see that in the VA at times. But most people are having 0, 1, 2, or maybe 3 or 4 visits a year. Then you know that is really a count. One of the things to think about when you are looking at it is to consider the data and the data generating process, because in terms of looking at counts, you could have something that is actually a mixed process and you may need to split the sample. 

This is an example that is totally unrelated to the VA, but it’s a good example of a mixed distribution. I recently saw a paper where someone was estimating the length of stay for all newborns. If you think about it, 90% of babies are well babies, and they all go home within 5 days. A batch of them will all go home within 3 days. That is clearly a count, and there is some variance in how quickly they go home. Then you take the sick newborns; some of them are only moderating sick. Or, if they die and will have short lengths of stay, but then others can have very long lengths of stay. Very small premature babies stay until they reach the general age of delivery so they can be there for two or three months, or even longer.  When you think about this, trying to model all those processes together, it is really two separate processes. You have the length of stay for the well babies who are going to go home quickly, and that is clearly a count. And then for the sick babies, you have a very different distribution. If you look at them jointly you are overlaying two distributions with two different data generating processes, then you are going to have a model that doesn’t work very well. You need to split your sample into well babies and sick babies and re-estimate it. This is just an example. There are other examples like this. The point I am really trying to make is when you are looking at something like this, is this really one data generating process, this generating the distribution of what I observed? In this case it is the length of stay. Or, is it something that is really two different processes that need to be modeled separately. That is something that all goes back to the basics of doing econometrics; you need to understand your data and the data generating processes. Look at your data carefully, and then set up your model accordingly. We have just touched on a few of the possibilities.

There are new methods coming up all of the time in terms of more and better ways to address the problems of limited dependent variables. This includes a growth in terms of semi-parametric and non-parametric methods that are more advanced than the old non-parametric methods, which tended to be very simplistic. You can now get some now that are the equivalent almost of a multi-variant type model in terms of what you control, but aren’t specifically parametric models. I just want to emphasize that when you have a problem where the dependent variables are not some big, continuous distribution with lots of variants and a relatively normal distribution, you need to look carefully at what should be modeled and how to model it. That is the end of the basic lecture.

In the slide set I have listed some reference texts. If you want a more general text, Jeff Wooldridge’s book on *Econometric Analysis of Cross Section and Panel Data* is excellent. And Maddala has a more dense shall I say textbook that is specifically focused on limited-dependent qualitative variables in econometrics. I also included the references for that McFadden test and for the Zhang model of converting the relative risks. The next lecture in this series is me again next week looking at Right-hand Side Variables. We will entertain questions. If anybody has any, you have to click on the orange arrow and use the question box to answer them. And Jean or Heidi will relay them to me and I will attempt to answer them.

Heidi or Jean:So far all we’ve gotten is, “Thanks. Great lecture. For our audience this is a great opportunity.” Oh, we just got a question in here. Will the mixed model be touched upon in subsequent lectures?

Ciaran Phibbs:Not to my knowledge. But I mean again, it’s the same method. It’s just that again you have to think about your data generating process. There is no formal test for this or anything like that. It’s really what one of my mentors referred to as the Art of Econometrics, as opposed to a science as to how to do this. There aren’t any hard and fast rules. You just have to know your data and think about your data carefully. That may effect how you approach the problem. In this case in the example I used, “I want to model this,” but then you get weirdness and you have to think, “No, there’s really two different processes.” It’s really two different samples of patients that you were trying to model jointly in the length of stay. And when you start combining very different samples, you can get problems if the processes driving the length of stay in that case are different, which they are.

Heidi or Jean:I have a question here, “Can we use count models when there are zeros in the data?”

Ciaran Phibbs:Oh yes.

Heidi or Jean:Do they all have to be greater than zero?

Ciaran Phibbs:No. I mean that’s one of the real strengths of a count data model is that it works much better than an OLS when you have lots of materials. I thought I had said that. One of the real problems with say I’m trying to model the number of falls that occur in a unit with the number of infections that occur in a unit where my observation is a patient, and most of the patients aren’t getting those infections. I have huge numbers and zeros, and OLS is very bad at that. Converting it to a rate when you are looking at your infection rates is a way to get around that problem, but even then you’re going to have zeros. A count data model is a much more efficient way to do it. The point estimates will be probably be fairly similar, but you are going to get a whole lot more statistical significance if you use a count data model.

Heidi or Jean:There’s another question here, “When looking at measuring relapse rates, I have used Cox regressions in the past. Do you have other suggestions?”

Ciaran Phibbs:A Cox regression is a time to event type model. That is a hazard model in terms of how long does it occur. The Cox regression is essentially measuring how long does it take for it to occur. So that is a different process, because you are trying to measure survival and what the crossover rates are. So that is a different process. That is another model that I did not touch on that is used frequently in health care and is relevant to this type of problem. It depends on, “Are you just interested in yes or no the event occurred?” Or, are you interested in how long it took for the event to occur. In which a Cox model is appropriate, or there is a class of models in terms of that survival model is the appropriate model.

Heidi or Jean:Somebody asked, “What about excess zeros in count models? Do I have to use the negatives if the zero is negative binomial?”

Ciaran Phibbs:The count models are explicitly designed to include zeros. And basically if you have lots of zeros, you are going to have bigger variants, so you are going to be away from the negative binomial. In terms of what distribution to actually use, I like to let Stata tell me how to handle that. They will even tell me, “No, negative binomial is not correct. You need to explore these other options, and it will help you figure that out.”

Heidi or Jean:So the negative binomial is a different option?

Ciaran Phibbs:Yes.

Heidi or Jean:There is a test for that, because that is another option?

Ciaran Phibbs:Yes.

Heidi or Jean:Somebody else asked, “Is there any rule of thumb when to switch from a multinomial model to a count model?”

Ciaran Phibbs:No, but those are different processes. Count models are for integers, and multinomial models are for choices. It can be ordered choices, but it’s choices. The choices in those models are totally different theoretical problems.

Heidi or Jean:Somebody asked, “I am planning on doing an analysis where I want to the model of medication ratio between zero and one. What do you recommend?”

Ciaran Phibbs:That’s something where the medication possession ratio can vary from zero to one, but it’s continuous. It’s not a zero or a one. And when you actually look at the data, you will get medical possession ratios occasionally that are greater than one. So that is more of a continuous distribution. The one thing that you need to check is to make sure that you have enough normality in your data. That’s an OLS type of thing, or some derivative of that. That’s a probability model. 

Heidi or Jean:Then somebody wants to know how can they sign up for the June 6th lecture.

Heidi or Jean:I just sent the announcement out like forty minutes ago. About half of our audience should have it in their e-mail right now. The other half should be getting it within the next hour or so. So just keep an eye on your e-mail, and it will show up there in just a moment.

Ciaran Phibbs:Assuming you got the e-mail for this one. If not, if for some reason you don’t get that, can you send them a link?

Heidi or Jean:We’ll send them the link. Yep.

Ciaran Phibbs:And if you send an e-mail to her, we’ll arrange to get it to you.

Heidi or Jean:There are no more questions right now.

Ciaran Phibbs:Okay. Well thank you everybody. I think we are probably loosing some attendance at this point, so see you at the same time next week. 

Heidi or Jean:Thank you so much Karen, and see you next week.

Ciaran Phibbs:Alright. I am going to sign off.

Page 1 of 13