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Lecture 8

SOC350H5 Lecture 8: Lecture 8

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University of Toronto Mississauga
David Pettinicchio

Lecture 8 Index Variable  Count data  Does not follow a distribution for OLS  How to create an index variable  People call it index/scale  Count measure  When creating scale  You ask spss to create scale, it will count what you categorize as 1  If you have victimization in random labels – need to recode data in the same direction so one in this variable is one in the other  Why is OLS problematic – too few variables added together you wont get statistical sig  It produces a small rage  Not enough variation in that range – due to less cases  Only go with adding index if you have five possible outcomes  Have to have enough variables  Things you add have to be same  How to create index  Start with clean and consistent variables  IF one variable is coded one and two – spss will just add two  When you add variables together they have to be exactly same otherwise adding things that are not comparable  Everything has to be same  Compute – add variables that you are going to add into total variable and use operations to add them  Will end up with a range  If you have 15 possibilities then max you can have is 15  Must not exceed the maximum  Have to also look at distribution  Always double check  For OLS it is problematic when there is little variation in that spread  Caveat – shouldn’t be doing OLS with count data  Because it is not a normal distribution  Can fix it to get significance  People that do index use cronbach’s alpha  Anything less than .7 means you have an unreliable scale Outliers  Normally dist data – symmetric – no influential outliers  Line of fit based on model that attempts to minimize error  Outliers have undue influence on the model (line of fit)  Outliers have large error and that effects slope  Model with mother and fathers occ pres and educ determining respondents occ pres  Doing a scatter plot on spss - most data is clustered  Everything that starts to move away could be problematic  Standardized residuals  Just because it seems to be an outlier doesn’t mean it is  Use standard residual tool – we want to compare errors  We want everything to be standardized  We are talking about the distance of points – that’s what we standardized  Allows us to talk about outliers beyond standard scores  Allows you to use normal dist to see if the outliers are beyond certain z scores  Those are def case for concerns – beyond 2.5 is problem  Idea is that you are now able to use properties of distributions to see how far stand dev away – 2.5 are problems  After creating new variable for distribution of variable – you can make a histogram  This is a distribution of the errors – not cases  0 is avg error and tails are stand dev away  When you go into spss – create new variable  This one has large outliers on positive end  Mean residual was 44.84  Lowest error -35.68  Highest was 56.901  Z score – -2.942 to 4.689  There is more problem on the right  Case that has highest error is 4.689 stand dev away from mean  Cases of homicide - ** Cook’s D  More systematic and another tool to see outliers is cooks d  A measure of both distance and leverage – how much of an influence is the case having on model  Higher the cook d value the more influence that case has on the slope and stat sig  Greater than 1 is not a problem but other ones are  Look at structure of data, using these tools are there cases that really stand out and might be influencing your model  Cook’s D – estimation diagnosis  Want to diagnose  Ranked in order DFbeta  What it does is look at difference between regression coefficient if you were to drop those outliers  It will give indicator – if you drop them, what would amount of influence of those cases be if you drop them  2/sq root of sample size OR greater than -1 or 1  Look at it comprehensively with all tests  0.04 as cutoff was established by 2/sqrtn Solutions  Delete the observation that is the outlier  Delete the variable if it has a lot of outliers  Transform a v
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