MCHB/EPI Miami Training — December 5 - 6, 2005

Creating Contiguity-Based Spatial Weights — Transcript

RAVI SHARMA: All right. We have figured out what was going on with the dissolve command. So Dianne is here. She's going to quickly take another look and do a dissolve command. And this time it's going to work.

DIANNE ENRIGHT: Right. This time it's going to work. It was just some kind of write error. But, again, talking about your health service regions and character text fields do work. Just wanted to be sure about that because in North Carolina I do this a lot for perinatal care regions and they always give me the data just by the name which is northwest, southwest. So — again in your toolbox under data management tools, generalization, there's a dissolve tool. And you select the shape file containing polygons that you want to use. And I'm going to put it to the default user. That was my problem before. And just give it a name. My health service field is checked on. And all I have to do is say okay.

RAVI SHARMA: Oh, whoa.

DIANNE ENRIGHT: And it pops in three regions.

RAVI SHARMA: Pennsylvania has been divided into three regions.

DIANNE ENRIGHT: If you want to see what the counties are underneath it. You can go to tool bars, get the effect tool bar and we can set the transparency for the regions to be lighter. Oops. The regions not the counties.

RAVI SHARMA: Isn't that cool?

UNKNOWN SPEAKER: That's neat.

RAVI SHARMA: That's cool.

UNKNOWN SPEAKER: That's cool.

DIANNE ENRIGHT: Okay.

RAVI SHARMA: Thank you, Dianne. (Whistling).

RAVI SHARMA: You got whistles.

DIANNE ENRIGHT: It does work. I promise.

RAVI SHARMA: Nobody whistled at me.

UNKNOWN SPEAKER: They will later.

RAVI SHARMA: No thank you.

Okay. So what I wanted to make sure is that you know we would like you to be also looking at some point at the slide presentation I have for GeoDa, because I can't, as I said, cover everything. But let me just go back and just refresh your memory as to what we did. This is creating the weights. So on my PowerPoint slide presentation you have a pretty detailed, I would say a blow by blow account of how you would go about doing, creating these weights. And it shows you exactly — they're all the different techniques for doing it. You know, this one is the nearest neighbor. And then what we're going to do next is to create — we're going to do, after creating a weight matrix, the next thing we want to do is do a special weight. A special weight is just using the weight matrix to smooth the rate for a particular county using information from surrounding counties. In other words, the term is we borrow strength from neighbors. Right? So that we — when we borrow strength from neighbors, we increase our numbers in the enumerator and the denominator. The assumption being it will be a little better rate. We'll do spatial rate, you know the instructions are to smooth special rate, invoke special smoothing. And here is spatial smoothed map is generated with LBW 92 and birth 92 and we can whatever rates we are interested in. So let's actually do it. So here's a data. So we're going to go to — if I see what we're doing here. I'm sorry. I can't even see.

Okay. That's not very clear. Is that very clear? It's not very clear.

UNKNOWN SPEAKER: Are you in space?

RAVI SHARMA: Let me just see. Let me see if I can — I don't think this moves. Focus. Can you try to focus here? I'll be good. That's better.

So what we're going to do is click on map. Smooth. Click on map. Make sure the map is selected. Click on map. Smooth. And we're going to do the spatial rate here. And as you can see, the dialog asks you for you to select an event variable and a base variable. So it makes it relatively easy to use this. So we're going to use — you can actually use whichever one you want. I'm going to use, let's say, I'm going to use the low birth weight for '92 and the birth for '02. Okay? So pick — just experiment. You don't have to use low birth weight in '92, just experiment with another year. So I have LBW 92 and birth '02. And please recall we've already set our weight matrix. We have already defined it as a queen weight matrix. And below here it's asking that you set your map team. That is how do you want to display the data from a smooth rate as a percentile map, quartile map or a box map with the following hinges, 1.5 or 3.0.

So let's do a quintile map here. You can use either one. Click okay. And we're going to take the default of 4 and say okay. So here is our smoothed map of low birth weight rate for '92. So we get some really interesting pattern here. You see this one is one, I hate to use the word cluster because we've not yet talked about it. But what you see is all these rates are in the upper quintile. And they all go together. And then this here is another cluster of counties with similarly high, and you see these two here. And this is our southeastern PA. Philadelphia . Is that Montgomery county? What counties are these? Montgomery ? Box. Good Lord, my geography is really good. Which is this, Delaware ?

UNKNOWN SPEAKER: Chester .

RAVI SHARMA: Chester , yeah. Good. Okay. So what you see immediately after you do your spatial smoothing and we've only used one year data it's even better if you use three year worth of data to do spatial smoothing. But I'm going to leave that as an exercise for you to do three years. So in a few minutes I'm going to have you do a three-year smoothed rate just to get you working with the field calculator calculating rates and then doing the spatial smoothing. Okay? So what you see here — so this is what immediately strikes you as here is that there is some pattern in your data. I mean that would be one immediate result based on spatial smoothing. What we're going to do is we're going to go back and do — so what is spatial smoothing? Spatial smoothing simply means you're borrowing strength from your neighbors. You're using neighbor data from a neighbor. We define neighbors as one order removed. So it's just one order of contiguity. So what you have there for is spatial smoothing based on simply using data from neighbors. That spatial smoothing we're going to now do — go back and click on map, smooth, and we're going to do an empirical base.

Now, if you recall, I'm just going to qualitatively talk about empirical base is based on this notion that you already know something about the distribution of your data. So it therefore uses the prior distribution, which is the distribution of births for Pennsylvania as a whole. So since Pennsylvania as a whole will tend to be more stable, because it is the large number of births, when you use the distributional properties for Pennsylvania as a whole and use that then to adjust individual rates for individual counties, you have what we call a shrinkage estimator. So the rates that are higher are shrunk to the middle while the low ones are moved up to the middle. So you have some shrinkage effects going on with this.

But the good thing about using empirical bases as you know this empirical base is different from what you learned in the usual statistic, which is the pre(inaudible) statistics. This includes — you don't have to worry about significant testing in this. This is a totally different way of looking at stability. Okay. So we are going to do the same. We're going to divide our event variable is going to be L births '92. Birth '92. We're going to do the quintile. Okay. And okay.

So here is your — so let me see if I can also open — I should have — we can actually — one way to have both the different maps side by side is to go and actually duplicate the map. If you use this one to duplicate the map, you can have four different maps displayed or five different maps displayed so you can look at the distribution separately.

So here is empirical base, which is slightly different way to smooth your data. You get a different picture, right? Slightly different picture. I mean look at what has happened to Allegheny county, which is it's now in the second quintile. But you know you see these — but you still see these clusters of counties in the high quintile and Philadelphia still is there and Chester and then you see some of these counties in the middle here. So that's the empirical base. Smoothed rate. Now, we can combine empirical base and spatial smoothing and calculate what we call empirically — so we can combine spatial and empirical base to calculate what we call spatial empirical base rates. So that's another one.

UNKNOWN SPEAKER: (Inaudible) what isn't that (inaudible) I'm asking.

RAVI SHARMA: This is purely statistical adjustment.

UNKNOWN SPEAKER: Okay.

RAVI SHARMA: This is purely statistical adjustment. It does not — in other words, you simply use the distribution of births. Prior distribution and adjust each. It's purely statistical. The spatial rate is purely spatial. You can combine the two. In other words, you know — which means you use strength from your neighbor and then the overall distribution and we will do that right now, which is create a — so if you go back here to map, smooth, you see this empirical, spatial empirical base.

UNKNOWN SPEAKER: Don't they use the weight?

RAVI SHARMA: They use the same weight. They still use the queen as the weight matrix.

UNKNOWN SPEAKER: Ravi , I have a question. (Inaudible) this morning how do we (inaudible) to smooth out? When is the time we (inaudible).

RAVI SHARMA: Well, the rule of the thumb normally is if you have small numbers — rule of the thumb. Less than ten. In Pennsylvania They use less than ten. My feeling is even if they're 20 or less than 20, you really need to — ten is more problematic. You really should adjust. Because what you will find is you can actually do simple, and I've done these: If you do confidence intervals, you will find they have very wide confidence intervals, which means the precision is very, very much in doubt. So, for example, I've already done here — before I do that let me see if I can go and show to you the — I have the upper and lower. So this is just for — this one up here is the lower confidence interval. And this one is the upper confidence interval. As you can see they go from seven to 11. So it's not too bad. You know, it's not too wide. But you can see there are some confidence intervals we can look at. Even these are not bad. Eight to ten. Ten to — so this is ten to — when I look at this — five to 15. Right? So I would worry about that. I mean that's too wide. So one way you, if you want to do it properly is there are different you know you can do it in SAS or different programs. You can actually calculate your confidence intervals and see, that will give you some idea of the precision. And this way you will decide, we'll give you added information about whether you should smooth or not smooth, if the confidence intervals are wide. The rule of thumb is the national center for health statistics will not — I'm trying to remember now. Is it ten? I know Pennsylvania if it's ten they will not publish anything. Am I right? Is it ten? Something like that.

UNKNOWN SPEAKER: Sometimes they use 20.

RAVI SHARMA: So you need to — in other words, what I would strongly recommend is you do confidence intervals. Calculate the standard errors for your rates and check the confidence intervals so you have added information before you go and actually smooth. So that's a good question. That's what I would recommend strongly.

UNKNOWN SPEAKER: You referred to the smoothing as borrowing strength. I'm wondering, are there confidence intervals for the smooth rates?

RAVI SHARMA: Understand, nobody calculates for the smoothed ones because —

UNKNOWN SPEAKER: You would think the precision would be better on it.

RAVI SHARMA: Yeah, yeah. You could call — I'm trying to think if people have calculated.

UNKNOWN SPEAKER: But that's not part of the geo data out there?

RAVI SHARMA: It's not. I'm trying to think. To calculate the confidence intervals I'm sure you will have the data to do it. But I'm not — but GeoDa doesn't do it. And I'm just trying to think —

RUSSELL KIRBY: There's extensive literature particularly about empirical bays in the bio statistical literature. I'm sure there's a way that you could calculate confidence intervals for the smoothed estimates. I'm not real familiar with what exactly that would be, but there's you know Lance Waller and Tom Lewis and Brad Carlin have published zillions of paper on historical issues with empirical base estimates. If you're interested in that you can look at the literature and I'm sure you could find a way that it could be done.

RAVI SHARMA: Yeah. Because this is just the way I calculated the upper and the lower. You can use the same kind of information you will need. But it will be easier — you don't have to do it by hand, right? It's easier if it can be done as part of the package. So I will check with Luke Anslon about that. There's an MCH list serve that everybody is on. So we can just send one.

UNKNOWN SPEAKER: I don't know the answer to that.

RAVI SHARMA: So what we'll do is for those of you here — I think it's an important question. We will put together a listing for all of you here and then send you an e-mail on that very particular question. And I'm curious whether you can do it. If maybe it can be done the next version of Luke Anslon who is the author of this, he's very open to people suggesting all kinds of bells and whistles to add and he will do it. And adding the confidence interval shouldn't be that big a deal.

UNKNOWN SPEAKER: (Inaudible).

RAVI SHARMA: Yes. Henry Lloyd's suggestion to have everybody's e-mails.

UNKNOWN SPEAKER: E-mail (inaudible).

RAVI SHARMA: All right. So we are — let's see, we are over here. We were going to do — yeah?

UNKNOWN SPEAKER: Can I ask a question (inaudible) maps, spatial and the smoothed spatial bays. What's the last one?

RAVI SHARMA: Last one we haven't done yet. The empirical spatial bays.

UNKNOWN SPEAKER: We've done it already.

RAVI SHARMA: Good.

UNKNOWN SPEAKER: Then we go over here in our counties where we're looking at our neighborhoods and stuff, I don't understand intuitively the difference between the spatial (inaudible) the ones with the spatial rate for the neighborhood or were they by Allegheny using the queen. They're all the same. Then using the empirical base.

RAVI SHARMA: Yes. And you know why, because there's different ways to smooth. So the spatial one essentially borrows from your spatial neighbors, and our spatial neighbors are one order removed.

UNKNOWN SPEAKER: Borrowed strength.

RAVI SHARMA: It means you add them together, exactly for each one separately.

UNKNOWN SPEAKER: And bays.

RAVI SHARMA: Bays is a purely statistical technique for adjustment. What it does is the empirical base thereom, what it says is simply you have some prior knowledge and your prior distribution is the distribution of births and births and births for Pennsylvania as a whole. So since we have a much larger distribution, your mean and your standard deviation and your variances are going to be much more stable than those for individual county. So we are going to empirical based theorem is why not use the information from this, what they call prior distribution and adjust the distribution of your low birth weight and births for each individual counties. So that, you know, very simply is the empirical base theorem. Now you can put those together so empirical base is purely statistical adjustment. You can put those two together which means borrow strength from your neighbors and which is spatial but also you can borrow strength from a much larger distribution of your area. So if your borrowing stems from two places and making your estimates a lot more stable.

UNKNOWN SPEAKER: (Inaudible).

RAVI SHARMA: Oops. Thank you.

UNKNOWN SPEAKER: What Windows is about to restart —

UNKNOWN SPEAKER: Probably being answered probably being bombarded right now with —

RAVI SHARMA: Thank you. I didn't want it to — geez. So let's see, we were going to do — did you already do the spatial empirical base. Then I don't need to do it. So here is what I would like you to do. This is your exercise.

I would like you, what I would like you to do is to aggregate the low birth weights for three years. So it will be 2000, 2001, 2002. We are then going to divide that by births for 2000, 2001 and 2002.

You're then going to multiply that by 100. Actually, let me make it a little more complex. This is fun here. I mean this is where you're going to learn. I want you to create two variables. One variable is simply an aggregation of births for those three years for 2000 to 2002. So just call it birth 00-00-02. That's one variable. Add a column. First thing you do is add a column. And call it births, low birth weight. LBW00200002 and create another column for births. 00002, call it whatever — feel free to name it whatever way you want so you can distinguish between the births and the deaths for those years. So we have two separate columns. And then we're going to use the field calculator to divide the number of births the number of low birth weights and the number of births.

Because now we have three aggregations. So to do that, you need to create another column, right? So that column will be, call it LBWR 00002. So you have three columns you're going to create. The third column will be the rate that you're going to calculate from your numerator and denominator. Does that make sense? . So this will be — you'll be using a lot of the tools here in GeoDa as a result of it.

So you have — I'll give you five minutes.

UNKNOWN SPEAKER: They probably need a little longer than that.

RAVI SHARMA: I'm just kidding. Ten minutes. 15? Let's turn the lights on. I'll be coming around giving you my personal assistance. We'll do it on the blackboard but I want you to get hands-on experience in doing this on your own.

All right. So shall we move to the next phase? The next phase is now that you have smoothed the arrays and gotten a visual, done visual exploratory data analysis, the next stage is to be able to detect. When you see patterns on your screen, you see what you think is a cluster. The next question is to ask yourself: Is it significant? Is it statistically significant or is it just a figment of your imagination or a figment of what you see.

So what you'll do in the next stages is I would like you to use the rates that you calculated, the rates that you calculated. What I would like you to do is to follow what I'm going to be talking to you about on the screen and you are going to do, first what we want to do is to do what's called the univariant moran. M-o-r-a-n. The univariant moran, if I can go back to, quickly, my presentation here by the way, those who are interested in what the weights look like. This is what the weights look like this is for county 0515 there are five neighbors and this is their, what you call Phipps code. That is an example of a weight matrix.

So let's see here. So we are now at this stage of identifying clusters and one of the most common tools for identifying a cluster, really the term we should use is spatial auto correlation, which is what we call feature similarity. It's based not only on feature location or attribute values alone but also on both feature location and feature values simultaneously. That simply means birth rates in Allegheny county compared to, sorry, low birth weight rates in Allegheny county compared to its neighbors. Both the low birth weights and the location. We're using both the feature location and the feature value simultaneously.

Given — so given a set of feature and associated attribute, if the value is where the pattern is expressed and random, in value random, near one indicates clustering and index value near minus one indicates dispersion. So you can have both positives and negatives because you can have a high value in one surrounded by a low value in another surrounding county.

But it goes from plus to minus one. And let's follow these directions here. So you're going to click on — you see the icon for univariant moran here. You're going to click on that. Click on — do you see it on your screen? Click on that. And the text block — so select your LBW, the raw rate. That's the rate that you created previously. So this is the one that you created for those three years. Okay?

Now the rate matrix remains the same because in the three years the counties have not changed. We still have 67 counties, right? So the neighborhood structure is still the same. We're still going to use the queen rate matrix. And when you run it, this should be — we'll get the results very similar to this. So run it.

So let's see. Okay. So what does it say? So you have — you have these four quadrants. This is a scatter plots results. By the way, you know what I should do here is I would like to acknowledge I have wonderful students in my class. And one of my students is Stacey Hofthorpe. She wanted to know if anybody is here from Wisconsin . She said she might know some people. She used to work in medicine. Do you know Stacey by any chance?

UNKNOWN SPEAKER: (Inaudible).

RAVI SHARMA: I'll let Stacey know.

UNKNOWN SPEAKER: I might be able to help with that.

RAVI SHARMA: Okay. So Stacey is one of my really wonderful students. She's a Ph.D. student in epidemiology. She's also getting a master's degree in computer and in information science. So you can imagine. I'm very proud of her. So she's partly responsible for —

UNKNOWN SPEAKER: You should have brought her.

RAVI SHARMA: So she's responsible for putting together this slide presentation. Just give her a few directions and off she went.

So what you see here are these four quadrants that represent — in this case what you see is a moran of.17. The question is, is that statistically significant. And we can test for it. So that's the next thing we're going to do. The four quadrants present special auto correlation, high-high. That's the high-high. Then you have the low-low for positive. High-high and low low for positive and high low for negative correlation. The plot is centered at the mean to test whether this is significant is very simple. Right click on the plot. Right click on the plot. And you can move to randomization, 919 permutation and you can see the permutation going on. And what do you see?

So you have — so click one to assess the sensitivity of the results. So you can run it again, by the way, to see how sensitive your results are. And now this P value is .002. So I would think that's significant. Although, the moran is low, but it's still you know highly significant.

And so that really is the univariant. Now, we call it global moran because it measures global pattern of clustering in your data. You may have local — you may have local clusters which it doesn't measure. But worry not because we have another tool for measuring local clusters. We call it LISA. It's local indicator of spatial auto correlation. But this is — so what you get in terms of your significance. Is it significant? No? What did you get? No.

UNKNOWN SPEAKER: Did you run that on '92 data or on the three year average?

RAVI SHARMA: That's one year. That's why — this is totally different, but you need to worry, look at your data and it shouldn't show any — so it should be pretty well —

UNKNOWN SPEAKER: I'm sorry, we want the LISA.

RAVI SHARMA: Now would you like to stand up and tell people how to do the LISA? Okay. So Lisa is a student in my class.

UNKNOWN SPEAKER: Is that right?

RAVI SHARMA: No, I'm just kidding. LISA is the abbreviation for Local Indication Spatial. LISA somebody thinks it's named for a wife, girlfriend or something like that. But no, nothing like that.

RAVI SHARMA: It measures local clustering. You can have, conceptually think about Pennsylvania as a whole. Six or seven counties. And what moran univariant moran as they call it, it measures the overall evidence of clustering. What it says is what your data shows is there is probably not a significant overall pattern of clustering. But there is — there may be localized clusters which univariant moran doesn't pick up. That's why Luke Anslon who developed LISA said we need to develop another tool that may pick up local clusters that might be significant.

So that's why we need to run — once you do the univariant to get the global picture and it's not significant, that doesn't mean that there isn't a pattern of local clustering. So the next step to do is to look at what we call local patterns of clusters. And for that we simply do the — oh, by the way, you can also do before we leave you can do this randomization, this envelope slopes, if you want to calculate. So envelope slopes simply, you can turn select envelope slope on to total randomization corresponding to 2.5% and 97.5% of Raster distribution so you get this envelope.

All right. So what we're going to do now, we're going to go on to LISA. Here's an explanation of what LISA is. Local moran or LISA, as I said before, Anslon, 1995, developed the local moran test to detect local area special autocorrelation. It can be used to identify local clusters, regions where adjacent areas have similar values or spatial outlier areas distinct from their neighbors. The local moran statistic decomposes the moran's eye into contributions from each location which is L sub I. The sum of L sub I for all observations is proportional to moran's eye, an indicator of global pattern. It can be two different interpretation of moran statistics as indicators of local and diagnostic tool for outliars in global spatial patterns.

So the morans, the local moran can tell you something about spatial clusters that maybe occurring at the local regional level but is also is a good diagnostic tool to focus on your attention on some clusters that maybe, well some areas, polygons which may be outliars in this global spatial patterns.

So to do the univariant moran is you simply click on the icon for the univariant local moran operation, which is right there. Some of you have already done it. And what you get is click on you — you get the significance map. You get the cluster out box, map, box plot and you get the local — you get the morans scatter plot. So you get a lot of information in one map here.

So please go ahead and do the local moran operation.

UNKNOWN SPEAKER: What's it stand for again.

RAVI SHARMA: Significance map with your LISA. And it tells you clusters that are significant at five — at 01. At .001 and at .001. Highly significant clusters. So what you see are clusters that are significant at up here — significant map shows location of significant local moran. So although you don't see globally, you do see some. But this is, you know, I find this interesting even though I haven't looked at the map. I mean we shouldn't again this data I put together you know for you to show you how to do it. Although I do work with this data, I will not read a lot into it. But this is interesting that you have the significant — these are all rural counties, by the way. This up here is this is McCain and I think this is Warren . And I do work in these counties. I've been doing community health assessments for them and I always make, crack this joke that there are more deer in those two counties than people. This is only a population of 5,000 in McCain County . It's really small. But all of us avoid driving through during the hunting season. Otherwise I wear one of those orange — is there a way to kill that?

UNKNOWN SPEAKER: I think what we need to do during the lunch hour is just —

RAVI SHARMA: Maybe let it update itself. All right. So here is one map. And as you will see, there's another map here. So this is the cluster map incorporates significant locations but they are now coded by type of spatial auto correlation, high-high remember low-low and low-low and high-high. So this is — so there are actually, this is interesting, all of these are low-low. So this is a low-low. And this one is — so there are really no high-high clusters. Mostly low-low.

The next one here —

UNKNOWN SPEAKER: Just a second.

RAVI SHARMA: Oops. What happened?

UNKNOWN SPEAKER: Normally when we look at a thematic map, things that are shaded the same are considered to be similar to one another. In this case are we just saying because if it's a similar shade like low-low, that the values are, what, very different compared to the neighbors?

RAVI SHARMA: No. No, this map is specifically constructed for LISA to show the existence. So what it is, is significant location, but now they're coded by spatial auto correlation. In other words low values go with low values and high values go with high values. When you do a corral plat there's no indication of that. This is specifically designed for showing the spatial auto correlation. So remember the four quadrants, high high, low low, high low. This is what it shows here now. Simply what it's doing it's plotting them on the map for you.

UNKNOWN SPEAKER: Right. I'm saying just because they're the same color doesn't mean they have the similar birth weight types, unlike the other —

RAVI SHARMA: No but what it shows is — no, no, this is low-low values together. Yes. No.

UNKNOWN SPEAKER: So we can't really infer about the low birth weight values it's all relational.

RAVI SHARMA: It's all relational but what it does show is that there's a low-low cluster. So in other words if — the low low wouldn't worry you as much as the high high. If it's a high high you want to do a little more investigation to find out what may be the underlying — if you have a group of counties, let's say five or six, you know, that shows high high cluster, that means they're bordering, spatially auto correlated but the correlation is such that the high values go with high values. Then you really want to look very closely to see if there is any underlying common patterns that may generate these high high clusters, because there may be a common source. Common etiology that may be responsible. So you probably want to do a little more in depth epidemiological investigation, right?

UNKNOWN SPEAKER: You mean like (inaudible).

RAVI SHARMA: Could be — exactly.

UNKNOWN SPEAKER: Do we have a group of them here that (inaudible).

RAVI SHARMA: Could be.

UNKNOWN SPEAKER: Could be racial ethnicity, poverty.

RAVI SHARMA: Yes. As you know when you do it in the cities Allegheny county or Pittsburgh , you will see clusters, and we know that is underlying is poverty. Race concentrated. But there is also environmental factors that may be operating, poor housing, you know —

UNKNOWN SPEAKER: Smoking.

RAVI SHARMA: Smoking, maternal smoking which could be potentially an important — so there are individual variables that may be responsible for these adverse outcomes, but there may be environmental variables at the same time. And to tease one from the other is a method logical challenge. I've shown you only one technique that are spatial. But if you want to include also individual level of variable there is what we call spatial multi-level modeling, which you can do.

UNKNOWN SPEAKER: How much caution do you have to exercise because you've got all this missing data, say, from your neighboring New York counties?

RAVI SHARMA: Yes. That depends — I mean you should always be cautious but it also depends on your underlying hypothesis. If you, when you say New York , you might be — are you saying that — I mean I can think of some ways that may be important. For example, if the births are — well, you know that's actually an interesting problem. But as you know the births in Pennsylvania I think a number of other states they are usually relocated to the place of the mother event, if it takes place outside — I know Pennsylvania, right, makes a conscious decision, goes to get all the births relocated back to where the mother is. So that shouldn't be a problem with low birth weight. But more important my questions might be if you're looking at underlying etiology, you know, environmental factors, that, again, that we go back to, you know, the edge effects. Because we're living — so, yeah, you're right. That may be a problem. If we're putting boundaries here that's not a good idea. So the edge effects might spill over. There may be spill over effect. So you should be careful. Yeah, Brian.

UNKNOWN SPEAKER: I think a couple of us came up with one county that's high high by itself. What does that mean?

RAVI SHARMA: That's interesting. I'll have to look at it. One county that's high high. So it has no neighbor?

UNKNOWN SPEAKER: Yeah, they've got the same —

RAVI SHARMA: Yeah. So may have to spend some time looking at that just to make sure there's no error here. Can you open the, what do you call it, the table? Open the table and click on that — go to Windows. And where is the table? That's good. Now, go down and click on the red and see which county is that. Cumberland . What's interesting about Cumberland ? What's the number of low birth weights?

UNKNOWN SPEAKER: Over the three years 554 low birth weight babies.

RAVI SHARMA: Really, that's a sizable number over three years. Now, what is —

UNKNOWN SPEAKER: But their rate is 8.2.

RAVI SHARMA: I mean, that's, you know, not low. That's —

UNKNOWN SPEAKER: It's right in there.

RAVI SHARMA: That still is —

UNKNOWN SPEAKER: I think it's possible to have a single county that is highlighted in relation to its neighbors but normally you'll find a cluster of counties, not just one, normally.

RAVI SHARMA: All right. So okay. I think finito.

UNKNOWN SPEAKER: Ask if there are any questions.

RAVI SHARMA: Finito.

UNKNOWN SPEAKER: I have a question. Again, the distinction of, I understand the LISA better than the global. What's the global tell you that's different, why would you want to look at that? Seems like it's an opposite. If we find an overall significance you look at that detail. This seems the opposite.

RAVI SHARMA: What do you think? (Inaudible) telling you different things. When you look at the global, it gives you a global picture. In other words, it's not searching for individual localized clusters. It's giving you an overall conceptually an overall picture of what the pattern is in your county. So there may be localized clusters, but if you use, when you use the local — it's really — so what they will pick up if they're very strong global patterns, that's what univariant moran will pick up, but it will not pick up local clusters.

UNKNOWN SPEAKER: (Inaudible).

UNKNOWN SPEAKER: So basically the bottom line is that you probably need to use a couple of these different techniques to really see what's going on in your data. You know, the moran's eye is just going to give you — it's analogous to if you are looking — say you have a data, an M by M table and you run a ki square on it it gives you an overall assessment —

RAVI SHARMA: Can we let this run?

RUSSELL KIRBY: Might as well now. That gives, the Ki square gives you an overall measure. But it doesn't tell you exactly where the pattern is. This is the same kind of thing that, the global tests give you the overall. But then if you really want to see within my map where are these areas that I really need to focus on.

RAVI SHARMA: Yeah. As you can see, in my little blurb, there's a relationship between local moran and moran. There's the relationship, right?

RUSSELL KIRBY: Other questions? Nobody has any other questions.

Okay. Well if there aren't any other questions I think Henry had a few announcements he wanted to give us and then it's about lunchtime.

Okay a few things that I need to let you know. That I'm still waiting for your evaluation. Got some of yours completed and I got it. So if you have completed yours before you go to lunch, let me have it. If not, you can complete it over lunchtime, after lunch, and let me after it. I would like to make sure that we all get it done.

Secondly, we've got a sub lunch today. It's ready. It's a different kind of lunch. You'll see it when you get there. Lunch will not be served in the Ocean View room. They gave us a different view so we see Miami as much as we could. So it will be a different view now. So we will go to bistro and the bar. You get to the hall here. Make a right turn. You'll see bistro and bar straight. Just go straight in there. It will be boxed lunch, and there will be some drinks there.

You can sit anywhere in the bar. If you don't want to sit there, you are free to walk outside and sit anywhere. That's what they told me. That's all I have to say. Thank you. And today we will try to end up early, about 4:00 . So afternoon curve and tea will be served about 2:30 .

Wait, the professor wanted to say something.

RUSSELL KIRBY: When you're filling out the evaluation forms, there are a few items on the evaluation I think it says we're going to EpiMap and we decided we didn't have time to do that. There's a couple other things, be aware of that. Please, if you have specific comments on how the session went, things that you would like — things we could have done better, things you would have liked to have, things that we didn't cover that you might like to know about, please write some comments because they're helpful to us in terms of devising additional trainings and I expect there will be additional trainings. So please do that.

UNKNOWN SPEAKER: And we'll be right here.