Topics

Topics

• Introduction to Stata– Files / directories– Stata syntax– Useful commands / functions

• Logistic regression analysis with Stata– Estimation– Goodness Of Fit– Coefficients – Checking assumptions

Introduction to Stata

• Note: we did this interactively for the larger part …

Stata file types

• .ado – programs that add commands to Stata

• .do– Batch files that execute a set of Stata commands

• .dta– Data file in Stata’s format

• .log– Output saved as plain text by the log using

command

The working directory

• The working directory is the default directory for any file operations such as using & saving data, or logging output

cd “d:\my work\”

Saving output to log files

• Syntax for the log command

log using [filename], replace text

• To close a log file

log close

Using and saving datasets

• Load a Stata dataset use d:\myproject\data.dta, clear

• Save save d:\myproject\data, replace

• Using change directorycd d:\myprojectuse data, clearsave data, replace

Entering data

• Data in other formats– You can use SPSS to convert data (read in or save

as a data file in another format, for instance Stata’s .dta format)

– You can use the infile and insheet commands to import data in ASCII format

• Entering data by hand– Type edit or just click on the data-editor button

Do-files

• You can create a text file that contains a series of commands. It is the equivalent of SPSS syntax (but way easier to memorize)

• Use the do-file editor to work with do-files

Adding comments in do-files

• // or * denote comments stata should ignore

• Stata ignores whatever follows after /// and treats the next line as a continuation

• Example II

A recommended template for do-files

capture log close //if a log file is open, close it, otherwise disregard

set more off //dont'pause when output scrolls off the page

cd d:\myproject //change directory to your working directory

log using myfile, replace text //log results to file myfile.log

… here you put the rest of your Stata commands …

log close //close the log file

Serious data analysis

• Ensure replicability use do+log files• Document your do-files

– What is obvious today, is baffling in six months• Keep a research log

– Diary that includes a description of every program you run

• Develop a system for naming files

Serious data analysis

• New variables should be given new names• Use variable labels and notes• Double check every new variable• ARCHIVE

Stata syntax examples

Stata syntax exampleregress y x1 x2 if x3<20, cluster(x4)

1. regress = command

– What action do you want to performed

2. y x1 x2 = Names of variables, files or other objects– On what things is the command performed

3. if x3 <20 = Qualifier on observations– On which observations should the command be

performed

4. , cluster(x4) = Options– What special things should be done in executing the

command

More examples

tabulate smoking race if agemother>30, row

More elaborate if-statements:

sum agemother if smoking==1 & weightmother<100

Elements used for logical statements

Operator Definition Example

== is equal in value to if male == 1

!= not equal in value to if male !=1

> greater than if age > 20

>= greater than or equal to if age >=21

< less than if age < 66

<= less than or equal to if age <=65

& and if age==21 & male==1

| or if age<=21 | age>=65

Missing values

• Automatically excluded when Stata fits models (same as in SPSS); they are stored as the largest positive values

• Beware!! – The expression “age>65” can thus also include

missing values (these are also larger than 65)– To be sure type: “age>65 & age!=.”

Selecting observations

drop [variable list]

keep [variable list]

drop if age<65

Note: they are then gone forever. This is not SPSS’s [filter] command.

Creating new variables

Generating new variables

generate age2 = age*age

(for more complicated functions, there also exists a command “egen”, as we will see later)

Useful functionsFunction Definition Example

+ addition gen y = a+b

- subtraction gen y = a-b

/ Division gen density=population/area

* Multiplication gen y = a*b

^ Take to a power gen y = a^3

ln Natural log gen lnwage = ln(wage)

exp exponential gen y = exp(b)

sqrt Square root gen agesqrt = sqrt(age)

Replace command

• replace has the same syntax as generate but is used to change values of a variable that already exists

gen age_dum = .replace age_dum = 0 if age < 5replace age_dum = 1 if age >=5

Recode

• Change values of existing variables

– Change 1 to 2 and 3 to 4 in origvar, and call the new variable myvar1: recode origvar (1=2)(3=4), gen(myvar1)

– Change 1’s to missings in origvar, and call the new variable myvar2:recode origvar (1=.), gen(myvar2)

Logistic regression

Logistic regression

• We use a set of data collected by the state of California from 1200 high schools measuring academic achievement.

• Our dependent variable is called hiqual. • Our predictor variable will be a continuous

variable called avg_ed, which is a measure of the average education (ranging from 1 to 5) of the parents of the students in the participating high schools.

OLS in Stata

_cons -.855187 .0363792 -23.51 0.000 -.9265637 -.7838102 avg_ed .4287064 .0127215 33.70 0.000 .4037467 .4536662 hiqual Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 254.263385 1157 .219760921 Root MSE = .33309 Adj R-squared = 0.4951 Residual 128.260563 1156 .110952044 R-squared = 0.4956 Model 126.002822 1 126.002822 Prob > F = 0.0000 F( 1, 1156) = 1135.65 Source SS df MS Number of obs = 1158

. regress hiqual avg_ed

. use "D:\Onderwijs\AMMBR\apilog.dta", clear

01

1 2 3 4 5avg parent ed

Fitted values Hi Quality School, Hi vs Not

. twoway scatter yhat hiqual avg_ed, connect(l) ylabel(0 1)

(42 missing values generated)(option xb assumed; fitted values). predict yhat

Logistic regression in Stata

_cons -12.30333 .731532 -16.82 0.000 -13.73711 -10.86956 avg_ed 3.910475 .2383352 16.41 0.000 3.443347 4.377603 hiqual Coef. Std. Err. z P>|z| [95% Conf. Interval]

Log likelihood = -353.94352 Pseudo R2 = 0.5156 Prob > chi2 = 0.0000 LR chi2(1) = 753.49Logistic regression Number of obs = 1158

Iteration 5: log likelihood = -353.94352 Iteration 4: log likelihood = -353.94352 Iteration 3: log likelihood = -353.94368 Iteration 2: log likelihood = -355.09635 Iteration 1: log likelihood = -386.86717 Iteration 0: log likelihood = -730.68708

. logit hiqual avg_ed

. twoway scatter yhat1 hiqual avg_ed, connect(l i) msymbol(i O) sort ylabel(0 1)

(42 missing values generated)(option pr assumed; Pr(hiqual)). predict yhat1

01

1 2 3 4 5avg parent ed

Pr(hiqual) Hi Quality School, Hi vs Not

)9.312( 111

1)|( Xe

XYE

Multiple predictors

_cons -12.05417 .739755 -16.29 0.000 -13.50407 -10.60428 avg_ed 3.86531 .2411152 16.03 0.000 3.392733 4.337887 yr_rnd -1.091038 .3425665 -3.18 0.001 -1.762456 -.4196197 hiqual Coef. Std. Err. z P>|z| [95% Conf. Interval]



. logit hiqual yr_rnd avg_ed

MODEL FIT

Consider model fit using:

1)The likelihood ratio test2)The pseudo-R2 (proportional change in log-likelihood)

3)The classification table

Model fit: the likelihood ratio test

)]baseline()New([22 LLLL

Model fit: LR test





764.88176. di 2*(-348.2462+730.68708)

Pseudo R2: proportional change in LL





.52339899

. di (730.68708-348.2462)/730.68708

A second measure of fit: the classification Table

Correctly classified 67.42% False - rate for classified - Pr( D| -) 32.58%False + rate for classified + Pr(~D| +) .%False - rate for true D Pr( -| D) 100.00%False + rate for true ~D Pr( +|~D) 0.00% Negative predictive value Pr(~D| -) 67.42%Positive predictive value Pr( D| +) .%Specificity Pr( -|~D) 100.00%Sensitivity Pr( +| D) 0.00% True D defined as hiqual != 0Classified + if predicted Pr(D) >= .5

Total 391 809 1200 - 391 809 1200 + 0 0 0 Classified D ~D Total True

Logistic model for hiqual

. estat class

Classification table for the model with the predictors

Correctly classified 87.31% False - rate for classified - Pr( D| -) 10.96%False + rate for classified + Pr(~D| +) 16.76%False - rate for true D Pr( -| D) 23.61%False + rate for true ~D Pr( +|~D) 7.43% Negative predictive value Pr(~D| -) 89.04%Positive predictive value Pr( D| +) 83.24%Specificity Pr( -|~D) 92.57%Sensitivity Pr( +| D) 76.39% True D defined as hiqual != 0Classified + if predicted Pr(D) >= .5

Total 377 781 1158 - 89 723 812 + 288 58 346 Classified D ~D Total True

Logistic model for hiqual

. estat class

Interpreting coefficients

Interpreting coefficients: significance



. logit hiqual yr_rnd avg_ed, nolog

bSE

b Wald

-16.29 = -12.05/0.74

Interpretation of coefficients: direction

------------------------------------------------------------------ avg_ed | 3.86531 16.031 0.000 47.7180 19.5978 0.7698 yr_rnd | -1.09104 -3.185 0.001 0.3359 0.6593 0.3819---------+-------------------------------------------------------- hiqual | b z P>|z| e^b e^bStdX SDofX------------------------------------------------------------------

Odds of: high vs not_high

logit (N=1158): Factor Change in Odds

. listcoef

nnxbxbxbbyp

yp

...

)(1

)(lnlogit 22110

Interpretation of coefficients: direction

------------------------------------------------------------------ avg_ed | 3.86531 16.031 0.000 47.7180 19.5978 0.7698 yr_rnd | -1.09104 -3.185 0.001 0.3359 0.6593 0.3819---------+-------------------------------------------------------- hiqual | b z P>|z| e^b e^bStdX SDofX------------------------------------------------------------------

Odds of: high vs not_high

logit (N=1158): Factor Change in Odds

. listcoef

nnxbxbxbb eeeeyp

yp

...

)(1

)(Odds 22110

Interpretation of coefficients: magnitude



. logit hiqual yr_rnd avg_ed, nolog

)yr_rnd1.1avg_ed9.312( 11

1)|(

eXYE

Interpretation of coefficients: Magnitude

)yr_rnd1.1avg_ed9.312( 11

1)|(

eXYE

yr_rnd 1200 .18 .3843476 0 1 avg_ed 1158 2.754212 .7697744 1 5 Variable Obs Mean Std. Dev. Min Max

. summ avg_ed yr_rnd

.08509905

. di 1/(1+exp(12-3.9*2.75+1.1))

.21840254

. di 1/(1+exp(12-3.9*2.75))

Assumptions and outliers

The link test (sort equivalent to linearity assumption in MR)

Multicollinearity (here we cheat a little)

Mean VIF 2.56 yr_rnd 1.11 0.903460 avg_ed 3.25 0.307731 meals 3.31 0.301982 Variable VIF 1/VIF

. vif

_cons .2445202 .0824989 2.96 0.003 .0826554 .4063849 meals -.0076084 .000527 -14.44 0.000 -.0086423 -.0065744 yr_rnd -.0008586 .0248112 -0.03 0.972 -.0495386 .0478215 avg_ed .1729601 .021089 8.20 0.000 .1315831 .2143371 hiqual Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 254.263385 1157 .219760921 Root MSE = .30632 Adj R-squared = 0.5730 Residual 108.279876 1154 .093830049 R-squared = 0.5741 Model 145.983509 3 48.6611696 Prob > F = 0.0000 F( 3, 1154) = 518.61 Source SS df MS Number of obs = 1158

. reg hiqual avg_ed yr_rnd meals

Influential observations: check the residuals

(42 missing values generated). predict stdres, rstand

(42 missing values generated)(option pr assumed; Pr(hiqual)). predict p

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0 .2 .4 .6 .8 1Pr(hiqual)

. scatter stdres p, mlabel(snum)

Have a closer look at the outlier residual

No 27 2.19 0 100 awards ell avg_ed hicred ym low medium medium . 808 824 59 28 cred_hl pared pared_ml pared_hl api00 api99 full some_col 1403 315 high high nd 100 497 low low 458. snum dnum schqual hiqual yr_rnd meals enroll cred cred_ml

. list if snum==1403

_cons -3.528875 1.037345 -3.40 0.001 -5.562035 -1.495716 avg_ed 2.010791 .2947269 6.82 0.000 1.433137 2.588445 meals -.0790397 .0076984 -10.27 0.000 -.0941283 -.0639511 yr_rnd -1.1328 .3842377 -2.95 0.003 -1.885892 -.3797077 hiqual Coef. Std. Err. z P>|z| [95% Conf. Interval]



. logit hiqual yr_rnd meals avg_ed if snum != 1403

_cons -3.566451 1.01715 -3.51 0.000 -5.560028 -1.572874 avg_ed 1.98805 .2884154 6.89 0.000 1.422766 2.553334 meals -.0758864 .0074453 -10.19 0.000 -.090479 -.0612938 yr_rnd -.9913148 .3743452 -2.65 0.008 -1.725018 -.2576117 hiqual Coef. Std. Err. z P>|z| [95% Conf. Interval]


. logit hiqual yr_rnd meals avg_ed, nolog

And this helps a little (but not much)

Assumptions (continued):

The model should fit equally well everywhere

Goodness of fit:Hosmer & Lemeshow

AverageProbabilityIn j th group

First logistic regression

_cons 2.425635 .3995025 6.07 0.000 1.642624 3.208645 cred_ml .7406536 .3152647 2.35 0.019 .1227463 1.358561 meals -.0936 .0084587 -11.07 0.000 -.1101786 -.0770213 yr_rnd -1.189537 .5022235 -2.37 0.018 -2.173877 -.2051967 hiqual Coef. Std. Err. z P>|z| [95% Conf. Interval]



. logit hiqual yr_rnd meals cred_ml

Then postestimation command

Prob > chi2 = 0.0000 Hosmer-Lemeshow chi2(8) = 40.45 number of groups = 10 number of observations = 707

10 0.9595 62 61.1 8 8.9 70 9 0.7531 44 43.5 26 26.5 70 8 0.4960 23 22.0 47 48.0 70 7 0.1554 4 7.4 68 64.6 72 6 0.0560 2 2.4 68 67.6 70 5 0.0208 1 0.9 71 71.1 72 4 0.0078 0 0.4 68 67.6 68 3 0.0037 0 0.2 71 70.8 71 2 0.0019 1 0.1 71 71.9 72 1 0.0008 1 0.0 71 72.0 72 Group Prob Obs_1 Exp_1 Obs_0 Exp_0 Total (Table collapsed on quantiles of estimated probabilities)

Logistic model for hiqual, goodness-of-fit test

. estat gof, table group(10)

Including interaction term helps...

_cons 2.686005 .4307661 6.24 0.000 1.841719 3.530291 ym .0463257 .0188326 2.46 0.014 .0094145 .0832368 cred_ml .7789823 .3206881 2.43 0.015 .1504452 1.407519 meals -.1019211 .0098691 -10.33 0.000 -.1212641 -.0825781 yr_rnd -2.834458 .8630901 -3.28 0.001 -4.526083 -1.142832 hiqual Coef. Std. Err. z P>|z| [95% Conf. Interval]


. logit hiqual yr_rnd meals cred_ml ym , nolog

. gen ym=yr_rnd*meals

... as you can see here

.

Prob > chi2 = 0.3215 Hosmer-Lemeshow chi2(8) = 9.25 number of groups = 10 number of observations = 707

10 0.9697 61 61.5 8 7.5 69 9 0.7725 44 43.4 25 25.6 69 8 0.4745 24 22.0 50 52.0 74 7 0.1420 2 6.5 66 61.5 68 6 0.0620 4 2.5 69 70.5 73 5 0.0204 1 1.0 70 70.0 71 4 0.0095 1 0.5 63 63.5 64 3 0.0054 0 0.3 74 73.7 74 2 0.0033 1 0.2 73 73.8 74 1 0.0015 0 0.1 71 70.9 71 Group Prob Obs_1 Exp_1 Obs_0 Exp_0 Total (Table collapsed on quantiles of estimated probabilities)

Logistic model for hiqual, goodness-of-fit test

. estat gof, table group(10)

Ok now

To do

• Perform a logistic regression analysis (check interaction effects as well!)

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