The other day I needed to conduct propensity score matching, but I was working with geographic data and wanted to restrict the matches to within a certain geographic distance. To do this I used the FUZZY extension command, which allows you to input a custom function. To illustrate I will be using some example data from my dissertation, and the code and data can be downloaded here.

So first lets grab the data and reduce it down a bit to only the variables we will be using. This dataset are street segments and intersections in DC, and the variables are crime, halfway houses, sidewalk cafes, and bars. Note to follow along you need to update the file handle to your machine.

```
FILE HANDLE save /NAME = "!!!Your Handle Here!!!".
GET FILE = "save\BaseData.sav".
DATASET NAME DC_Data.
SORT CASES BY MarID.
*Reduce the variable list down a bit.
MATCH FILES FILE = * /KEEP MarID XMeters YMeters OffN1 OffN2 OffN3 OffN4 OffN5 OffN6 OffN7 OffN8 OffN9
TotalCrime HalfwayHouse SidewalkCafe TypeC_D.
```

Now as a quick illustration, I am going to show a propensity score analysis predicting the location of halfway houses in DC – and see if street units with a halfway house are associated with more violence. Do not take this as a serious analysis, just as an illustration of the workflow. The frequency shows there are only 9 halfway houses in the city, and the compute statements collapse crimes into violent and non-violent. Then I use `PLUM`

to fit the logistic model predicting the probability of treatment. I use non-violent crimes, sidewalk cafes, and bars as predictors.

```
FREQ HalfwayHouse.
COMPUTE Viol = OffN1 + OffN4 + OffN5 + OffN6.
COMPUTE NonViol = OffN2 + OffN3 + OffN7 + OffN8 + OffN9.
*Fitting logit model via PLUM.
PLUM HalfwayHouse WITH NonViol SidewalkCafe TypeC_D
/CRITERIA=CIN(95) DELTA(0) LCONVERGE(0) MXITER(100) MXSTEP(5) PCONVERGE(1.0E-6) SINGULAR(1.0E-8)
/LINK=LOGIT
/PRINT=FIT PARAMETER SUMMARY
/SAVE=ESTPROB.
```

The model is very bad, but we can see that sidewalk cafes are never associated with a halfway house! (Again this is just an illustration – don’t take this as a serious analysis of the effects of halfway houses on crime.) Now we need to make a custom function with which to restrict matches not only based on the probability of treatment, but also based on the geographic location. Here I made a file named `DistFun.py`

, and placed in it the following functions:

```
#These functions are for SPSS's fuzzy case control matching
import math
#distance under 500, and caliper within 0.02
def DistFun(d,s):
dx = math.pow(d[1] - s[1],2)
dy = math.pow(d[2] - s[2],2)
dis = math.sqrt(dx + dy)
p = abs(d[0] - s[0])
if dis < 500 and p < 0.02:
t = 1
else:
t = 0
return t
#distance over 500, but under 1500
def DistBuf(d,s):
dx = math.pow(d[1] - s[1],2)
dy = math.pow(d[2] - s[2],2)
dis = math.sqrt(dx + dy)
p = abs(d[0] - s[0])
if dis < 1500 and dis > 500 and p < 0.02:
t = 1
else:
t = 0
return t
```

The FUZZY command expects a function to return either a 1 for a match and 0 otherwise, and the function just takes a fixed set of vectors. The first function `DistFun`

, takes a list where the first two elements are the coordinates, and the last element is the probability of treatment. It then calculates the euclidean distance, and returns a 1 if the distance is under 500 and the absolute distance in propensity scores is under 0.02. The second function is another example if you want matches not too close but not too far away, at a distance of between 500 and 1500. (In this dataset my coordinates are projected in meters.)

Now to make the research reproducible, what I do is save this python file, `DistFun.py`

, in the same folder as the analysis. To make this an importable function in SPSS for FUZZY you need to do two things. ~~1) Also have the file ~~ (Jon Peck made the comment this is not necessary), and 2) add this folder to the system path. So back in SPSS we can add the folder to `__init__.py`

in the same folder`sys.path`

and check that our function is importable. (Note that this is not permanent change to the `PATH`

system variable in windows, and is only active in the same SPSS session.)

```
*Testing out my custom function.
BEGIN PROGRAM Python.
import sys
sys.path.append("!!!Your\\Path\\Here!!!\\")
import DistFun
#test case
x = [0,0,0.02]
y = [0,499,0.02]
z = [0,500,0.02]
print DistFun.DistFun(x,y)
print DistFun.DistFun(x,z)
END PROGRAM.
```

Now we can use the FUZZY command and supply our custom function. Without the custom function you could specify the distance in any one dimension on the FUZZ command (e.g. here something like `FUZZ = 0.02 500 500`

), but this produces a box, not a circle. Also with the custom function you can do more complicated things, like my second buffer function. The function takes the probability of treatment along with the two spatial coordinates of the street unit.

```
*This uses a custom function I made to restrict matches to within 500 meters.
FUZZY BY=EST2_1 XMeters YMeters SUPPLIERID=MarID NEWDEMANDERIDVARS=Match1 Match2 Match3 GROUP=HalfwayHouse CUSTOMFUZZ = "DistFun.DistFun"
EXACTPRIORITY=FALSE
MATCHGROUPVAR=MGroup
/OPTIONS SAMPLEWITHREPLACEMENT=FALSE MINIMIZEMEMORY=TRUE SHUFFLE=TRUE SEED=10.
```

This takes less than a minute, and in this example provides a full set of matches for all 9 cases (not surprising, since the logistic regression equation predicting halfway house locations is awful). Now to conduct the propensity score analysis just takes alittle more data munging. Here I make a second data of just the matched locations, and then reshape the cases and controls so they are in long format. Then I merge the original data back in.

```
*Reshape, merge back in, and then conduct outcome analysis.
DATASET COPY PropMatch.
DATASET ACTIVATE PropMatch.
SELECT IF HalfwayHouse = 1.
VARSTOCASES /MAKE MarID FROM MarID Match1 Match2 Match3
/INDEX Type
/KEEP MGroup.
*Now remerge original data back in.
SORT CASES BY MarID.
MATCH FILES FILE = *
/TABLE = 'DC_Data'
/BY MarID.
```

Now you can conduct the analysis. For example most people use t-tests both for the outcome and to assess balance on the pre-treatment variables.

```
*Now can do your tests.
T-TEST GROUPS=HalfwayHouse(0 1)
/MISSING=ANALYSIS
/VARIABLES=Viol
/CRITERIA=CI(.95).
```

One of my next projects will be to use this workflow to conduct fuzzy name matching within and between police databases using custom string distance functions.

## camdenln

/ May 20, 2015Very cool. Another use of custom functions with FUZZY that I have seen is where the user wanted the match to be asymmetric.

Two things to watch out for in custom functions: if missing data are a possibility, be sure to handle that case. Second, the custom function will be called a huge number of times if the datasets are large, so it should be written as efficiently as possible. If it is complicated, it might be worth memoizing it.

One final point: if you have added the directory holding the function to the search path, there is no need to provide an __init__.py file.

Jon Peck

## apwheele

/ May 20, 2015All good points – will update to say there is no need for the init file. Part of the reason I save the custom function in the same folder with the analysis is so I don’t lose it! (Or accidentally have multiple functions roaming around.) It makes it easier to share code this way as well.

Memoization is likely to test my programming abilities, but exiting the function earlier is an easier step.