Stata 11 whitepaper mwp 4 mwp mwp-028 / 41 mwp mwp mwp-079 functions 72 mwp-076 insheet 89 mwp-030 recode 94 mwp-033 reshape wide

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1 PS001

2 Stata 11 whitepaper mwp 4 mwp mwp-028 / 41 mwp mwp mwp-079 functions 72 mwp-076 insheet 89 mwp-030 recode 94 mwp-033 reshape wide/long 100 mwp-036 ivregress 110 mwp-082 logistic/logit 127 mwp-039 logistic/logit 137 mwp-040 margins 151 mwp-029 mlogit 167 mwp-090 ologit 184 mwp-088 poisson 199 mwp-087 regress 217 mwp-037 regress 235 mwp-038 anova/oneway 247 mwp-042 sdtest χ 2 F 272 mwp-043 ttest t 279 mwp-041 table 286 mwp-070 tabstat 294 mwp-071 tabulate 299 mwp-072 tabulate 305 mwp-073

3 StataCorp c 2011 Math c 2011 StataCorp LP Math web: [email protected]

4 mwp-076 functions - Stata generate [D] functions [D] egen (mwp-077 ) Running sum t 3.2 t / 7. c Copyright Math c Copyright StataCorp LP (used with permission) 4

5 1. Stata [D] functions Random-number functions 1.1 runiform() [0, 1) (observations) 10 x 1 repeatability seed. set obs 10 obs was 0, now 10. set seed 2. generate x1 = runiform() * 1. list * 2 x [a, a + b) a + b*runiform() [10, 20) x 2 *1 Data Create or change data Create new variable *2 Data Describe data List data 5

6 . generate x2 = *runiform(). list x2 x round() floor(). generate x3 = round(x2). list x2 x3 x2 x round() floor() runiform(). generate x4 = round( *runiform()). list x4 x

7 Stata [D] functions Mathematical functions 2.1 round() floor() ceil() int() 0 (1) x round(x) floor(x) ceil(x) int(x) x = x = int() floor() (2) x round(x) floor(x) ceil(x) int(x) x = x = int() ceil() 7

8 2.2 Running sum sum() running sum 1, 2,..., 10 x. clear. set obs 10. generate x = n * 3 x running sum. generate y1 = sum(x). list x y y 1 i j=1 x j (i = 1, 2,..., 10) egen total() 10 j=1 x j. egen y2 = total(x) * 4. list x y1 y *3 n [U] 13.4 System variables *4 Data Create or change data Create new variable (extended) 8

9 3. Stata [D] functions Probability distributions and density functions Student t 3.1 t Example fuel.dta t. use clear * wide mpg1 mpg2. list, separator(0) mpg1 mpg mpg1 = mpg2 t 5% *5 File Example Datasets Stata 11 manual datasets Base Reference Manual [R] ttest 9

10 . ttest mpg1 == mpg2 * 6. ttest mpg1 == mpg2 Paired t test Variable Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] mpg mpg diff mean(diff) = mean(mpg1 mpg2) t = Ho: mean(diff) = 0 degrees of freedom = 11 Ha: mean(diff) < 0 Ha: mean(diff)!= 0 Ha: mean(diff) > 0 Pr(T < t) = Pr( T > t ) = Pr(T > t) = mpg1 mpg t p ttest [R] ttest (mwp-041 ) 3.2 t tden(n, t) t t n n 11. twoway (function tden(11, x), range(-4 4)), ytitle("") xtitle(t) > title(t(11) distribution) * 7 *6 Statistics Summaries, tables and tests Classical tests of hypotheses Mean-comparison test, paired data *7 Graphics Twoway graph (scatter, line, etc.) 10

11 ttest t > Stata [D] functions Programming functions 4.1 / recode(), autocode(), irecode() age01.dta. use 11

12 . list, separator(0) age (1) recode() recode() (x, x 1, x 2,..., x n ) x 1, x 2,..., x n x. generate code1a = recode(age, 20, 30, 40, 50, 60, 70, 80, 90). list age code1a, separator(0) age code1a x 1, x 2,..., x n x > x n. generate code1b = recode(age, 25, 40, 60). list age code1b, separator(0) age code1b x > x n x n 12

13 (2) autocode() (3) irecode() 5. Stata [D] functions String functions 6. / Data Editor 10/15/ jan jan1960 daily() monthly() [D] functions Date and time functions mwp Stata [D] functions Matrix functions returning a matrix Matrix functions returning a scalar A = matrix input A = (1,1,1\1,2,2\1,2,3). matrix list A symmetric A[3,3] c1 c2 c3 r1 1 r2 1 2 r A A inv() 13

14 . matrix B = inv(a). matrix list B symmetric B[3,3] r1 r2 r3 c1 2 c2 1 2 c A 1 = A Cholesky cholesky(). matrix C = cholesky(a). matrix list C C[3,3] c1 c2 c3 r r r CC T. matrix D = C*C. matrix list D symmetric D[3,3] r1 r2 r3 r1 1 r2 1 2 r A = CC T 14

15 mwp-082 ivregress - OLS 1. OLS 2. OLS ivregress SLS 6.3 LIML 6.4 GMM 7. ivregress postestimation 7.1 estat endogenous 7.2 estat firststage 7.3 estat overid 1. OLS y i = β 0 + β 1 x i + u i, i = 1, 2,..., n (M1) β 0 β 1 2 (OLS: ordinary least squares) 4 c Copyright Math c Copyright StataCorp LP (used with permission) 15

16 x (fixed variable) u 0 E(u i ) = 0, i = 1, 2,..., n (M2) V (u i ) = E(u 2 i ) = σ 2, i = 1, 2,..., n (M3) Cov(u i, u j ) = E(u i u j ) = 0, i j, i, j = 1, 2,..., n (M4) OLS 2 (RSS: residual sum of squares) n n RSS = (y i ŷ i ) 2 = (y i ˆβ 0 ˆβ 1 x i ) 2 (M5) i=1 i=1 ˆβ 0, ˆβ 1 RSS ˆβ 0 RSS ˆβ 1 n = 2 (y i ˆβ 0 ˆβ 1 x i ) = 0 (M6a) i=1 n = 2 (y i ˆβ 0 ˆβ 1 x i )x i = 0 (M6b) i=1 ˆβ 0, ˆβ 1 n i=1 ˆβ 1 = (x n i x)(y i ȳ) i=1 n (= (x ) i x)y i=1 (x i i x) 2 n i=1 (x i x) 2 ˆβ 0 = ȳ ˆβ 1 x (M7a) (M7b) 2. OLS (1) (unbiasedness) θ ˆθ ˆθ E(ˆθ) θ E(ˆθ) = θ (M8) ˆθ (unbiased estimator) 1 4 OLS ˆβ 0, ˆβ 1 (BLUE: best linear unbiased estimator) [ Gauss-Markov ] 16

17 (2) (consistency) n ˆθ θ ϵ > 0 lim P ( ˆθ θ ϵ) = 0 n ˆθ θ (consistent estimator) ˆθ θ ˆθ θ OLS ˆβ 0, ˆβ 1 plim ˆθ = θ (M9) 3. 1 (1) x (M7a) y i ȳ = β 1 (x i x) + (u i ū) ˆβ 1 = n i=1 (x i x)(y i ȳ) n i=1 (x i x) 2 = β 1 + n i=1 (x i x)(u i ū) n i=1 (x i x) 2 (M10) [ n E[ ˆβ i=1 1 ] = β 1 + E (x ] i x)(u i ū) n i=1 (x i x) 2 (M11) 2 x u 0 x u 0 ˆβ 1 β 1 (2) [ n ] plim(v (x i )) = plim (x i x) 2 /n = σx 2 i=1 [ n ] plim(cov(x i, u i )) = plim (x i x)(u i ū)/n = σ xu i=1 17

18 (M10) [ n plim( ˆβ i=1 1 ) = plim β 1 + (x ] i x)(u i ū) n i=1 (x i x) 2 = β 1 + plim [ n i=1 (x ] i x)(u i ū)/n n i=1 (x i x) 2 /n = β 1 + plim [ n i=1 (x i x)(u i ū)/n] plim [ n i=1 (x i x) 2 /n] = β 1 + σ xu σ 2 x (M12) σ xu 0 x u ˆβ 1 β 1 (3) 2 ξ η η i = β 0 + β 1 ξ i + ϵ i, i = 1, 2,..., n η ξ x i y i y i = β 0 + β 1 x i + u i, i = 1, 2,..., n x i ξ i + v i v i u i = ϵ i β 1 v i Cov(x i, u i ) = Cov(ξ i + v i, ϵ i β 1 v i ) = β 1 σv 2 0 x u OLS (4) Y C I { Yi = C i + I i C i = β 0 + β 1 Y i + u i I (exogenous variable) Y i = β 0 1 β β 1 I i β 1 u i C i = β 0 1 β 1 + β 1 1 β 1 I i β 1 u i Y 18

19 Y u [ ] u 2 Cov(Y i, u i ) = E i = σ2 0 1 β 1 1 β 1 (endogenous variable) OLS ivregress 7. ivregress postestimation 19

20 mwp-037 regress - regress regress. regress mpg weight foreign Source SS df MS Number of obs = 74 F( 2, 71) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = mpg Coef. Std. Err. t P> t [95% Conf. Interval] weight foreign _cons c Copyright Math c Copyright StataCorp LP (used with permission) 20

21 Stata Example auto.dta mpg = β 0 + β 1 weight + β 2 foreign + ϵ Stata regress 1.1 regress1.dta 1,000 use 5. list in 1/5 * 1 y x1 x2 x y. generate y = 0.5*x1 + 2*x rnormal(0, 10) x 1 x 2 rnormal(m, s) m s [D] functions y = 0.5x x 2 10 (1) x 1, x 2 x 3 y x 3 *1 Data Describe data List data 21

22 1.2 1,000 regress Statistics Linear models and related Linear regression Model : Dependent variable: y Independent variables: x1 x2 x3 1 regress - Model. regress y x1 x2 x3 Source SS df MS Number of obs = 1000 F( 3, 996) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = y Coef. Std. Err. t P> t [95% Conf. Interval] x x x _cons (1) regress n(n 3) 2 rvfplot 22

23 . rvfplot, yline(0) * 2 (x 1i, x 2i,...) ŷ i y i y i ŷ i rvfplot (residual-versus-fitted plot) ŷ i 10 (2) R 2 regress regress ANOVA y SS (sum of squares) y i (i = 1,..., n) ȳ 2 y i ŷ i y (yi ȳ) 2 = (y i ŷ i ) 2 + (ŷ i ȳ) 2 (2) (yi ȳ) 2 TSS (total sum of squares) (ŷi ȳ) 2 MSS (model sum of squares) (yi ŷ i ) 2 RSS (residual sum of squares) TSS MSS RSS *2 Statistics Linear models and related Regression diagnostics Residual-versus-fitted plot 23

24 (coefficient of determination) R 2 = MSS TSS = 1 RSS TSS (3) / = ANOVA R-squared 39% (3) p R-squared 1 p Prob > F (ANOVA: analysis of variance) F H 0 H 0 : β 1 = β 2 = = 0 β 0 (4) ANOVA Coef. (coefficients) β 1 = 0.48 β2 = 1.97 β3 = 0.01 β0 = 8.91 (1) (5) p p β j = 0 t p x 3 p β 3 = 0 β 3 95% CI: confidence interval [ 0.21, 0.22] 0 x 3 x 1, x 2 p 0 regress p x postestimation 1 test Statistics Postestimation Tests Test linear hypotheses Main : Test type for specification 1: Linear expressions are equal Specification 1, linear expression: x1 =

25 2 test - Main. test (x1 = 0.5) ( 1) x1 =.5 F( 1, 996) = 0.62 Prob > F = (6) Coef. (standard error) Std. Err. (standard deviation) x 1 95% CI (degrees of freedom) 996 t invttail(n, p) [D] functions. display invttail(996, 0.025) * % (critical value). display * display * x 1 95% CI [ , ] *3 Data Other utilities Hand calculator 25

26 x 1, x ,000 1/10 resampling seed seed. set seed 111 * sample 100, count * 5 (900 observations deleted) 100 regress. regress y x1 x2 x3. regress y x1 x2 x3 Source SS df MS Number of obs = 100 F( 3, 96) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = y Coef. Std. Err. t P> t [95% Conf. Interval] x x x _cons R 2 x x % test *4 [R] set seed *5 Statistics Resampling Draw random sample 26

27 . test (x1 = 0.37). test (x1 = 0.37) ( 1) x1 =.37 F( 1, 96) = 3.65 Prob > F = test (x1 = 0.8). test (x1 = 0.8) ( 1) x1 =.8 F( 1, 96) = 3.74 Prob > F = p 0.05 (significance level) 5% Reporting Confidence level 3 2. Stata Example auto.dta. sysuse auto.dta * 6 (1978 Automobile Data) mpg (miles per gallon) weight 2 weight 2 2 c.weight#c.weight mwp-028. generate weightsq = weight^2 * 7 *6 File Example datasets Example datasets installed with Stata *7 Data Create or change data Create new variable 27

28 . format weightsq %10.0g * 8. list mpg weight weightsq in 1/5 * 9 mpg weight weightsq , , , , , weight K 2 2. regress mpg weight weightsq * 10. regress mpg weight weightsq Source SS df MS Number of obs = 74 F( 2, 71) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = mpg Coef. Std. Err. t P> t [95% Conf. Interval] weight weightsq 1.32e e e e 06 _cons mpg = 1.42e-2 weight e-6 weight mpg weight weight weight (normalize) 0 1 beta *8 Variables weightsq Format weightsq *9 Data Describe data List data *10 Statistics Linear models and related Linear regression 28

29 regress : Reporting : Standardized beta coefficients: 3 regress - Reporting. regress mpg weight weightsq, beta Source SS df MS Number of obs = 74 F( 2, 71) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = mpg Coef. Std. Err. t P> t Beta weight weightsq 1.32e e _cons beta weight weight

30 3. auto.dta weight length β 0 length = 0 β 0 β 0 = 0 noconstant Statistics Linear models and related Linear regression Model : Dependent variable: weight Independent variables: length Suppress constant term:. regress weight length, noconstant Source SS df MS Number of obs = 74 F( 1, 73) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = weight Coef. Std. Err. t P> t [95% Conf. Interval] length Example census9.dta. use clear * 11 (1980 Census data by state) *11 File Example Datasets Stata 11 manual datasets Base Reference Manual [R] regress 30

31 . list state drate pop medage region in 1/5, nolabel * 12 state drate pop medage region 1. Alabama 91 3,893, Alaska , Arizona 78 2,718, Arkansas 99 2,286, California 79 23,667, (drate) (medage) (region) region Northeast, North Central, South, West 1, 2, 3, 4 drate medage pop mwp regress - Weights Analytic weights Frequency weights Alabama 3, 893, *12 region 31

32 Statistics Linear models and related Linear regression Model : Dependent variable: drate Independent variables: medage i.region * 13 Weights : Analytic weights: pop. regress drate medage i.region [aweight = pop] (sum of wgt is e+08) Source SS df MS Number of obs = 50 F( 4, 45) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = drate Coef. Std. Err. t P> t [95% Conf. Interval] medage region _cons [aweight = pop] 5. regress 2 (OLS: ordinary least squares) OLS (homoskedasticity) Example auto.dta. sysuse auto, clear (1978 Automobile Data). replace weight = weight/1000 * 14 *13 i. mwp-028 *14 Data Create or change data Change contents of variable K 32

33 . regress mpg weight. regress mpg weight Source SS df MS Number of obs = 74 F( 1, 72) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = mpg Coef. Std. Err. t P> t [95% Conf. Interval] weight _cons twoway (scatter mpg weight) (lfit mpg weight), ytitle(mpg) * 15 1 rvpplot (residual-versus-predictor plot). rvpplot weight, yline(0) * 16 *15 Graphics Twoway graph (scatter, line, etc.) *16 Statistics Linear models and related Regression diagnostics Residual-versus-predictor plot 33

34 rvpplot weight (heteroskedasticity) Statistics Postestimation Reports and statistics estat : Reports and statistics: Tests for heteroskedasticity (hettest) 5 estat 34

35 . estat hettest Breusch Pagan / Cook Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of mpg chi2(1) = Prob > chi2 = estat hettest H 0 p H 0 OLS OLS regress SE/Robust SE (standard error) Statistics Linear models and related Linear regression Model : Dependent variable: mpg Independent variables: weight SE/Robust : Robust 6 regress - SE/Robust 35

36 . regress mpg weight, vce(robust) Linear regression Number of obs = 74 F( 1, 72) = Prob > F = R squared = Root MSE = Robust mpg Coef. Std. Err. t P> t [95% Conf. Interval] weight _cons vce(robust) OLS 95% CI OLS Robust weight [ 7.04, 4.98] [ 7.17, 4.84] cons [36.22, 42.66] [35.48, 43.40] SE/Robust Clustered robust 36

37 5 Graphics Twoway graph (scatter, line, etc.) Plots Create Plot 1 Choose a plot category and type: Basic plots Basic plots: Scatter Y variable: mpg X variable: weight Plots Create Plot 2 Choose a plot category and type: Fit plots Fit plots: Linear prediction Y variable: mpg X variable: weight Y axis : Title: mpg. twoway (scatter mpg weight) (lfit mpg weight), ytitle(mpg) 37

38 mwp-042 anova/oneway - anova oneway ANOVA ANOVA oneway 4. ANOVA anova ANOVA 7. ANOVA 8. ANOVA 1. 2 t mwp A, B, C t α 5% (1) A-B = 0.95 (2) A-C = 0.95 (3) B-C = = 0.86 (1), (2), (3) = % c Copyright Math c Copyright StataCorp LP (used with permission) 38

39 3 (ANOVA: analysis of variance) F (multiple comparison) 2. (1) (2) (3) (4) (repeated-measures) ANOVA 3. ANOVA oneway (factor) 1 ANOVA (one-way ANOVA) ANOVA anova, oneway oneway anova1.dta. use clear 24 (blood pressure). list if n <= 3 n >= 22, separator(3) * 1 bp drug drug 1, 2, 3, 4 4 drug *2 *1 Data Describe data List data *2 Stata 39

40 drug bp oneway α 5% Statistics Linear models and related ANOVA/MANOVA One-way ANOVA Main : Response variable: bp Factor variable: drug Multiple-comparison tests: Bonferroni Output: Produce summary table: 1 oneway - Main 40

41 . oneway bp drug, bonferroni tabulate Summary of bp drug Mean Std. Dev. Freq Total Analysis of Variance Source SS df MS F Prob > F Between groups Within groups Total Bartlett's test for equal variances: chi2(3) = Prob>chi2 = Comparison of bp by drug (Bonferroni) Row Mean Col Mean (1) ANOVA tabulate (frequency) 6 oneway anova (unbalanced data) ANOVA Analysis of Variance Source SS df MS F Prob > F Between groups Within groups Total Bartlett's test for equal variances: chi2(3) = Prob>chi2 =

42 SS (sum of squares) regress mwp-037 y (yi ȳ) 2 = (y i ŷ i ) 2 + (ŷ i ȳ) 2 (yi ȳ) 2 TSS (total sum of squares) (ŷi ȳ) 2 MSS (model sum of squares) (yi ŷ i ) 2 RSS (residual sum of squares) MSS (between groups) RSS (within groups) TSS (total) (df: degrees of freedom) MS (mean square) , F /54.16 = 3.92 F F p p < 0.05 ANOVA Bartlett ANOVA p 0.05 (2) ANOVA µ 1 = µ 2 = µ 3 = µ 4 bonferroni Bonferroni ANOVA Comparison of bp by drug (Bonferroni) Row Mean Col Mean M ij M ij µ i µ j 0 Bonferroni p µ 4 µ 2 Bonferroni Scheffe, Šidák 42

43 4. ANOVA anova ANOVA 7. ANOVA 8. ANOVA ANOVA 43

44 mwp-070 table - table Superrows, supercolumns 1. table table table n n (n-way table) n 7 (frequency) (mean) (standard deviation) (maximum) (minimum) (median) (interquantile range) (percentile) c Copyright Math c Copyright StataCorp LP (used with permission) 44

45 2. Example auto.dta. sysuse auto.dta * 1 (1978 Automobile Data) displacement. generate disp1 = 16.4*displacement/1000 * 2 disp1. summarize disp1 * 3. summarize disp1 Variable Obs Mean Std. Dev. Min Max disp l 7.0l disp1 class class 0 disp < disp < disp < disp1. generate class = irecode(disp1, 2.0, 3.0, 4.0) * 4 5 disp1 class. list make disp1 class in 1/5 make disp1 class 1. AMC Concord AMC Pacer AMC Spirit Buick Century Buick Electra *1 File Example datasets Example datasets installed with Stata *2 Data Create or change data Create new variable *3 Statistics Summaries, tables and tests Summary and descriptive statistics Summary statistics *4 irecode() [D] functions 45

46 class mpg (miles per gallon) Statistics Summaries, tables, and tests Tables Table of summary statistics (table) Main : Row variable: class Statistics 1: Count nonmissing mpg Statistics 2: Mean mpg Statistics 3: Standard deviation mpg 1 table - Main. table class, contents(count mpg mean mpg sd mpg ) class N(mpg) mean(mpg) sd(mpg) mpg class *5 *5 Variables Manager 46

47 . label define class 0 "<2000cc" 1 " cc" 2 " cc" 3 ">4000cc". label values class class. table class, contents(count mpg mean mpg sd mpg ). table class, contents(count mpg mean mpg sd mpg ) class N(mpg) mean(mpg) sd(mpg) <2000cc cc cc >4000cc table Options Options : Override display format for numbers in cells: %9.2f 2 table - Options. table class, contents(count mpg mean mpg sd mpg ) format(%9.2f) class N(mpg) mean(mpg) sd(mpg) <2000cc cc cc >4000cc

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