1. Basic Introduction LOGISTIC REGRESSION
Mike Bailey
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2. Course at statistics.com
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3. BASICS Response dichotomous Predictors X
categorical (usually make these dichotomous
Design variables)
real-valued
Predictors X
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4. PREDICTING PROBABILITIES
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5. LOGISTIC MODEL
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6. LOGIT FUNCTION
So, if we can estimate p(x) and take the logit, we have a linear
function of the x’s. We can use regression to estimate b’s
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7. ODDS
p(x)/(1-p(x)) is the ODDS that Y=1 given x
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8. CASE 1: DICHOTOMOUS x data contingency table Y X 1 Y=0 Y=1 X=0 a d X=1
data
contingency table
Y=0
Y=1
X=0 a d
X=1 c b
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9. ODDS
what are the odds of Y=1 when X=1?
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10. ODDS RATIO when X=1 when X=0
Y=0
Y=1
X=0 a d
X=1 c b
when X=1
when X=0
ratio of odds
for Y = 1
odds ratios have easily-understood interpretation
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11. EXAMPLE Y = 1 if the baby has low birth weight
X = 1 if the mother has frequent prenatal care
ODDS RATIO: the increase in P[Y=1] when X=1
“Low birth weight occurs half as often (O.R. = ½) when the mother has adequate prenatal care.”
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13. THE MAGIC CONTINUES... b1 = ln(O. R.) the logit is linear in x
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14. USING R G <- glm(formula = weight ~ prenatal,
family = binomial(link = logit) )
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15. DATA Save out of Excel as a .csv filey x1 x2 x3 x4 x5
marine
army
navy
iraqi
200 1
100 90
300 50
150
Save out of Excel as a .csv file
> eof2 <-read.csv(file="e:datafile2.csv", header = TRUE)
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16. RESULTS
> g2 <- glm(formula = y ~ x1+x2+x3+x4+x5, family = binomial(link=logit), data = eof2)
> g2
Call: glm(formula = y ~ x1 + x2 + x3 + x4 + x5, family = binomial(link = logit), data = eof)
Coefficients:
(Intercept) x x x x x5 NA
Degrees of Freedom: 36 Total (i.e. Null); 32 Residual
Null Deviance:
Residual Deviance: AIC: 13.8
H0: The model doesn’t explain the variability in the data
Deviance statistic ~ sum of squares ~ c2
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17. ARMY vs. USMC
> SERV2 <- glm(formula = y ~ marine + army, family = binomial(link=logit), data = eof2)
> SERV2
Call: glm(formula = y ~ marine + army, family = binomial(link = logit), data = eof2)
Coefficients:
(Intercept) marine army
-1.757e e e-09
Degrees of Freedom: 36 Total (i.e. Null); 34 Residual
Null Deviance:
Residual Deviance: AIC: 34.71
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18. AOR
> region2 <- glm(formula = y ~ raleigh + topeka + denver + mobile + oshkosh + eagle, family = binomial(link=logit), data = eof2)
> region2
Call: glm(formula = y ~ raleigh + topeka + denver + mobile + oshkosh eagle, family = binomial(link = logit), data = eof2)
Coefficients:
(Intercept) raleigh topeka denver mobile oshkosh eagle
-1.957e e e e e e NA
Degrees of Freedom: 36 Total (i.e. Null); 31 Residual
Null Deviance:
Residual Deviance: AIC: 32.84
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19. EXAMPLE Fear of Violence in Children
Y = 1 iff the interview-ee anticipates being the victim of violence in the next 6 months
Predictors are demographic
Age (Design variable, 2-year categories)
Race (Design variable)
Below the Poverty Line (Dichotomous)
Sex (Dichotomous)
Two-parent home (Dichotomous)
Recent victim (Dichotomous)
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20. EXAMPLE Fear of Violence in Children
source: poster display, Gornto Teletechnet Center, ODU
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21. EARLY SEXUAL EXPERIENCE AND IQ
Y=1 if the subject had sexual experience
Predictors (X) are...
design variables for intervals of the AHVPT (IQ)
design variables for age (HS, Undergrad, Grad)
design variables for specific universities
source:
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22. RESULTS
IQ of 100 was 5x more likely to have intercourse than an IQ 130 (odds ratios)
Each IQ point increases the odds of virginity by 2.7% for males, 1.7% for females (estimates of b)
Probability of virginity (predicted values of Y)
Age 19 males: 20%
Age 19 females: 25%
College aged: 13%
Princeton undergrads: 44%
Harvard undergrads: 41%
MIT graduate students: 35%
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23. RESULTS
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24. SUMMARY
Logistic regression produces odds ratios, predicted values, and regression coefficients
Odds ratios are easily interpreted
Predictors (x’s) are often categorical or dichotomous
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