Survey
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1 Types of Surveys Cross-sectional • surveys a specific population at a given point in time • will have one or more of the design components • stratification • clustering with multistage sampling • unequal probabilities of selection Longitudinal • surveys a specific population repeatedly over a period of time • panel • rotating samples 2 Cross Sectional Surveys Sampling Design Terminology 3 Methods of Sample Selection Basic methods • simple random sampling • systematic sampling • unequal probability sampling • stratified random sampling • cluster sampling • two-stage sampling 4 Simple Random Sampling 0 10 20 30 40 50 60 70 80 90 100 Why? • basic building block of sampling • sample from a homogeneous group of units How? • physically make draws at random of the units under study • computer selection methods: R, Stata 5 Systematic Sampling 0 10 20 30 40 50 60 70 80 90 100 Why? • easy • can be very efficient depending on the structure of the population How? • get a random start in the population • sample every kth unit for some chosen number k 6 Additional Note Simplifying assumption: • in terms of estimation a systematic sample is often treated as a simple random sample Key assumption: • the order of the units is unrelated to the measurements taken on them 7 Unequal Probability Sampling Why? • may want to give greater or lesser weight to certain population units • two-stage sampling with probability proportional to size at the first stage and equal sample sizes at the second stage provides a self-weighting design (all units have the same chance of inclusion in the sample) How? • with replacement • without replacement 8 With or Without Replacement? • in practice sampling is usually done without replacement • the formula for the variance based on without replacement sampling is difficult to use • the formula for with replacement sampling at the first stage is often used as an approximation Assumption: the population size is large and the sample size is small – sampling fraction is less than 10% 9 Stratified Random Sampling 0 10 20 30 40 50 60 70 80 90 100 Why? • for administrative convenience • to improve efficiency • estimates may be required for each stratum How? • independent simple random samples are chosen within each stratum 10 Example: Survey of Youth in Custody • first U.S. survey of youths confined to long-term, state-operated institutions • complemented existing Children in Custody censuses. • companion survey to the Surveys of State Prisons • the data contain information on criminal histories, family situations, drug and alcohol use, and peer group activities • survey carried out in 1989 using stratified systematic sampling 11 SYC Design strata • type (a) groups of smaller institutions • type (b) individual larger institutions sampling units • strata type (a) • first stage – institution by probability proportional to size of the institution • second stage – individual youths in custody • strata type (b) • individual youths in custody • individuals chosen by systematic random sampling 12 Cluster Sampling 0 10 20 30 40 50 60 70 80 90 100 Why? • convenience and cost • the frame or list of population units may be defined only for the clusters and not the units How? • take a simple random sample of clusters and measure all units in the cluster 13 Two-Stage Sampling 0 10 20 30 40 50 60 70 80 90 100 Why? • cost and convenience • lack of a complete frame How? • take either a simple random sample or an unequal probability sample of primary units and then within a primary take a simple random sample of secondary units 14 Synthesis to a Complex Design Stratified two-stage cluster sampling Strata • geographical areas First stage units • smaller areas within the larger areas Second stage units • households Clusters • all individuals in the household 15 Why a Complex Design? • better cover of the entire region of interest (stratification) • efficient for interviewing: less travel, less costly Problem: estimation and analysis are more complex 16 Ontario Health Survey • carried out in 1990 • health status of the population was measured • data were collected relating to the risk factors associated with major causes of morbidity and mortality in Ontario • survey of 61,239 persons was carried out in a stratified two-stage cluster sample by Statistics Canada 17 OHS Sample Selection • strata: public health units – divided into rural and urban strata • first stage: enumeration areas defined by the 1986 Census of Canada and selected by pps • second stage: dwellings selected by SRS • cluster: all persons in the dwelling 18 Longitudinal Surveys Sampling Design 19 Schematic Representation Panel Survey 4 Time 3 2 1 0 Respondents 20 Schematic Representation Rotation Survey 4 Time 3 2 1 0 Respondents 21 British Household Panel Survey Objectives of the survey • to further understanding of social and economic change at the individual and household level in Britain • to identify, model and forecast such changes, their causes and consequences in relation to a range of socio-economic variables. 22 BHPS: Target Population and Frame Target population • private households in Great Britain Survey frame • small users Postcode Address File (PAF) 23 BHPS: Panel Sample • designed as an annual survey of each adult (16+) member of a nationally representative sample • 5,000 households approximately • 10,000 individual interviews approximately. • the same individuals are re-interviewed in successive waves • if individuals split off from original households, all adult members of their new households are also interviewed. • children are interviewed once they reach the age of 16 • 13 waves of the survey from 1991 to 2004 24 BHPS: Sampling Design Uses implicit stratification embedded in two-stage sampling • postcode sector ordered by region • within a region postcode sector ordered by socioeconomic group as determined from census data and then divided into four or five strata Sample selection • systematic sampling of postcode sectors from ordered list • systematic sampling of delivery points (≈ addresses or households) 25 BHPS: Schema for Sampling 26 Survey Weights 27 Survey Weights: Definitions initial weight • equal to the inverse of the inclusion probability of the unit final weight • initial weight adjusted for nonresponse, poststratification and/or benchmarking • interpreted as the number of units in the population that the sample unit represents 28 Interpretation Interpretation • the survey weight for a particular sample unit is the number of units in the population that the unit represents Not sampled, Wt = 2, Wt = 5, Wt = 6, Wt = 7 29 Effect of the Weights • Example: age distribution, Survey of Youth in Custody Sum of Age Counts Weights 11 1 28 12 9 149 13 53 764 14 167 2143 15 372 3933 16 622 5983 17 634 5189 18 334 2778 19 196 1763 20 122 1164 21 57 567 22 27 273 23 14 150 24 13 128 Totals 2621 25012 30 Unweighted Histogram Age Distribution of Youth in Custody 0.3 Proportion 0.25 0.2 0.15 0.1 0.05 0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Age 31 Weighted Histogram Age Distribution of Youth in Custody 0.3 Proportion 0.25 0.2 0.15 0.1 0.05 0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Age 32 Weighted versus Unweighted Proportion Weighted and Unweighted Histograms 0.3 0.25 0.2 0.15 0.1 0.05 0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Age Weighted Unweighted 33 Observations • the histograms are similar but significantly different • the design probably utilized approximate proportional allocation • the distribution of ages in the unweighted case tends to be shifted to the right when compared to the weighted case • older ages are over-represented in the dataset 34 Survey Data Analysis Issues and Simple Examples from Graphical Methods 35 Basic Problem in Survey Data Analysis 36 Issues iid (independent and identical distribution) assumption • the assumption does not not hold in complex surveys because of correlations induced by the sampling design or because of the population structure • blindly applying standard programs to the analysis can lead to incorrect results 37 Example: Rank Correlation Coefficient Pay equity survey dispute: Canada Post and PSAC • two job evaluations on the same set of people (and same set of information) carried out in 1987 and 1993 • rank correlation between the two sets of job values obtained through the evaluations was 0.539 • assumption to obtain a valid estimate of correlation: pairs of observations are iid 38 Scatterplot of Evaluations Rank in 1993 200 100 0 0 100 200 Rank in 1987 • Rank correlation is 0.539 39 A Stratified Design with Distinct Differences Between Strata • the pay level increases with each pay category (four in number) • the job value also generally increases with each pay category • therefore the observations are not iid 40 Scatterplot by Pay Category Rank in 1993 200 2 3 4 5 100 0 0 100 Rank in 1987 200 41 Correlations within Level Correlations within each pay level • Level 2: –0.293 • Level 3: –0.010 • Level 4: 0.317 • Level 5: 0.496 Only Level 4 is significantly different from 0 42 Graphical Displays first rule of data analysis • always try to plot the data to get some initial insights into the analysis common tools • histograms • bar graphs • scatterplots 43 Histograms unweighted • height of the bar in the ith class is proportional to the number in the class weighted • height of the bar in the ith class is proportional to the sum of the weights in the class 44 Body Mass Index measured by • weight in kilograms divided by square of height in meters • 7.0 < BMI < 45.0 • BMI < 20: health problems such as eating disorders • BMI > 27: health problems such as hypertension and coronary heart disease 45 BMI: Women 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 BMI 11 14 17 20 23 26 29 32 35 38 41 44 46 BMI: Men 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 BMI 11 14 17 20 23 26 29 32 35 38 41 44 47 BMI: Comparisons 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 BMI 11 14 17 20 23 26 Women 29 32 35 38 41 44 Men 48 Bar Graphs Same principle as histograms unweighted • size of the ith bar is proportional to the number in the class weighted • size of the ith bar is proportional to the sum of the weights in the class 49 Ontario Health Survey Distribution of Levels of Happiness by Marital Status Marital Status Divorced Widowed Single Married 0% 20% 40% 60% 80% 100% Percentage Happy Somewhat happy Somewhat unhappy Unhappy Very unhappy 50 Scatterplots unweighted • plot the outcomes of one variable versus another problem in complex surveys • there are often several thousand respondents 51 10 20 BMI 30 40 Scatterplot of BMI by Age and Sex 20 30 40 50 60 Age 52 Solution • bin the data on one variable and find a representative value • at a given bin value the representative value for the other variable is the weighted sum of the values in the bin divided by the sum of the weights in the bin 53 25 24 23 Binned-BMI 26 27 BMI Trends by Age and Sex 0 10 20 30 40 Age 54 Bubble Plots • size of the circle is related to the sum of the surveys weights in the estimate • more data in the BMI range 17 to 29 approximately DBMI versus BMI (binned) 30 DBMI 25 20 15 12 22 32 BMI 42 55 Computing Packages STATA and R 56 Available Software for Complex Survey Analysis • commercial Packages: • STATA • SAS • SPSS • Mplus • noncommercial Package •R 57 STATA defining the sampling design: svyset – example svyset [pweight=indiv_wt], strata(newstrata) psu(ea) vce(linear) – output: pweight: indiv_wt VCE: linearized Strata 1: newstrata SU 1: ea FPC 1: <zero> 58 R: survey package • define the sampling design: svydesign – wk1de<svydesign(id=~ea,strata=~newstrata,weight=~i ndiv_wt,nest=T,data=work1) • output > summary(wk1de) Stratified 1 - level Cluster Sampling design With (1860) clusters. svydesign(id = ~ea, strata = ~newstrata, weight = ~indiv_wt, nest = T, data = work1) 59 Syntax • STATA: – – – – svy: estimate Example: least squares estimation svyset [pweight=indiv_wt], strata(newstrata) psu(ea) svy: regress dbmi bmi • R: – svy***(*, design, data=, ...) – Example: least squares estimation – wk2de<svydesign(id=~ea,strata=~newstrata,weight=~indiv_wt, nest=T,data=work2) – svyglm(dbmi~bmi, data=work2,design=wk2de) 60 Available Survey Commands R STATA Descriptive Yes Yes Regression Yes Yes (More) Resampling Yes Yes Longitudinal Yes No PMLE Yes Yes Calibration Yes No 61 Survey Data Analysis Contingency Tables and Issues of Estimation of Precision 62 General Effect of Complex Surveys on Precision • stratification decreases variability (more precise than SRS) • clustering increases variability (less precise than SRS) • overall, the multistage design has the effect of increasing variability (less precise than SRS) 63 Illustration Using Contingency Tables • two categorical variables that can be set out in I rows and J columns • can get a survey estimate of the proportion of observations in the cell defined by the ith row and jth column: p̂ij 64 Example: Ontario Health Survey • rows: five levels describing levels of happiness that people feel • columns: four levels describing the amount of stress people feel • Is there an association between stress and happiness? 65 STATA Commands use "I:\workshopjune\work.dta", clear svyset [pweight=indiv_wt], strata(newstrata) psu(ea) svy: tabulate happiness stress (running tabulate on estimation sample) Number of strata Number of PSUs = = 72 1860 Number of obs Population size Design df = 48057 = 7961780.7 = 1788 66 STATA Output • table on stress and happiness • estimated proportions in the table with test statistic ------------------------------------------------------| stress happiness | 1 2 3 4 Total ----------+-------------------------------------------1 | .042 .2567 .2856 .085 .6692 2 | .026 .1426 .0935 .0109 .2731 3 | .0106 .0246 .0085 8.5e-04 .0446 4 | .004 .0045 .0015 8.4e-04 .0108 5 | .0016 3.4e-04 2.0e-04 2.1e-04 .0023 | Total | .0841 .4288 .3893 .0978 1 ------------------------------------------------------Key: cell proportions Pearson: Uncorrected Design-based chi2(12) = 3674.8280 F(8.66, 15484.10)= 89.2775 P = 0.0000 67 Possible Test Statistics adapt the classical test statistic • need the sampling distribution of the statistic Wald Test • need an estimate of the variance-covariance matrix 68 Estimation of Variance or Precision • variance estimation with complex multistage cluster sample design: • exact formula for variance estimation is often too complex; use of an approximate approach required • NOTE: taking account of the design in variance estimation is as crucial as using the sampling weights for the estimation of a statistic 69 Some Approximate Methods • Taylor series methods • Replication methods • Balanced Repeated Replication (BRR) • Jackknife • Bootstrap 70 Replication Methods • you can estimate the variance of an estimated parameter by taking a large number of different subsamples from your original sample • each subsample, called a replicate, is used to estimate the parameter • the variability among the resulting estimates is used to estimate the variance of the full-sample estimate • covariance between two different parameter estimates is obtained from the covariance in replicates • the replication methods differ in the way the replicates are built 71 Assumptions The resulting distribution of the test statistic is based on having a large sample size with the following properties • the total number of first stage sampled clusters (or primary sampling units) is assumed large • the primary sample size in each stratum is small but the number of strata is large • the number of primary units in a stratum is large • no survey weight is disproportionately large 72 Possible Violations of Assumptions • the complex survey (stratified two-sample sampling, for example) was done on a relatively small scale • a large-scale survey was done but inferences are desired for small subpopulations • stratification in which a few strata (or just one) have very small sampling fractions compared to the rest of the strata • The sampling design was poor resulting in large variability in the sampling weights 73 Survey Data Analysis Linear and Logistic Regression 74 General Approach • form a census statistic (model estimate or expression or estimating equation) • for the census statistic obtain a survey estimate of the statistic • the analysis is based on the survey estimate 75 Regression Use of ordinary least squares can lead to • badly biased estimates of the regression coefficients if the design is not ignorable • underestimation of the standard errors of the regression coefficient if clustering (and to a lesser extent the weighting) is ignored 76 Example: Ontario Health Survey Regress desired body mass index (DBMI) on body mass index (BMI) STATA Unweighted Weighted Intercept Estimate S.E. 10.877 0.141 11.196 0.064 10.877 0.065 Slope Estimate S.E. 0.4958 0.0058 0.4716 0.0025 0.4858 0.0026 77 Simple Linear Regression Model • typical regression model y i α β x i ei E(e i ) 0, E(e ) σ , E(e ie j ) 0 2 i 2 • linear relationship plus random error • errors are independent and identically distributed 78 Census Statistic • census estimate of the slope parameter N B β̂ (x i 1 i X)(y i Y) N 2 (x X ) i i 1 • Problem: the assumption of independent errors in the population does not hold • Solution: the least squares estimate is a consistent estimate of the slope 79 Survey Estimate • the census estimate B is now the parameter of interest • the survey estimate is given by b ˆ )(y Y ˆ) w (x X i i i i ˆ )2 w (x X i i i • estimate obtained from an estimating equation • the estimate of variance cannot be taken from the analysis of variance table in the regression of y on x using either a weighted or unweighted analysis 80 Variance Estimation Again, estimate of the variance of b is obtained from one of the following procedures • Taylor linearization • Jackknife • BRR • Bootstrap 81 Issues in Analysis • application of the large sample distributional results • small survey • regression analysis on small domains of interest • multicollinearity • survey data files often have many variables recorded that are related to one another 82 Multicollinearity Example: Ontario Health Survey Two regression models: regress desired body mass index on • actual body mass index, age, gender, marital status, smoking habits, drinking habits, and amount of physical activity • all of the above variables plus interaction terms: marital status by smoking habits, marital status by drinking habits, physical activity by age 83 Partial STATA Output No interaction terms -----------------------------------------------------------------------------| Linearized dbmi | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------bmi | .4375517 .0066716 65.58 0.000 .4244667 .4506368 age | .0157202 .0014647 10.73 0.000 .0128475 .0185929 _Imarital_2 | .1413547 .0498052 2.84 0.005 .0436718 .2390377 _Imarital_3 | .4752516 .1416521 3.36 0.001 .1974293 .7530739 _Imarital_4 | -.0349268 .0749697 -0.47 0.641 -.1819648 .1121113 _Isex_2 | -2.192169 .036238 -60.49 0.000 -2.263243 -2.121095 Interaction terms present -----------------------------------------------------------------------------| Linearized dbmi | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------bmi | .4369983 .0066473 65.74 0.000 .4239608 .4500357 age | .0027515 .0045811 0.60 0.548 -.0062335 .0117364 _Imarital_2 | .020803 .283399 0.07 0.941 -.5350276 .5766337 _Imarital_3 | .8300453 .3153888 2.63 0.009 .2114731 1.448618 _Imarital_4 | -.486307 .4478352 -1.09 0.278 -1.364646 .3920324 84 _Isex_2 | -2.193464 .0362143 -60.57 0.000 -2.264491 -2.122437 Comparison of Domain Means Domains and Strata • both are nonoverlapping parts or segments of a population • usually a frame exists for the strata so that sampling can be done within each stratum to reduce variation • for domains the sample units cannot be separated in advance of sampling Inferences are required for domains. 85 Regression Approach • use the regression commands in STATA and declare the variables of interest to be categorical • example: DBMI relative to BMI related to sex and happiness index STATA commands use "I:\workshopjune\work.dta", clear svyset [pweight=indiv_wt], strata(newstrata) psu(ea) . . xi:svy: regress ratio i.sex*i.happiness i.sex _Isex_1-2 (naturally coded; _Isex_1 omitted) i.happiness _Ihappiness_1-5 (naturally coded; _Ihappiness_1 omitted) i.sex*i.happi~s _IsexXhap_#_# (coded as above) (running regress on estimation sample) 86 STATA Output -----------------------------------------------------------------------------| Linearized ratio | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------_Isex_2 | -.0555096 .0022378 -24.81 0.000 -.0598986 -.0511206 _Ihappines~2 | .0036588 .0033689 1.09 0.278 -.0029487 .0102663 _Ihappines~3 | .0038151 .0082526 0.46 0.644 -.0123708 .0200009 _Ihappines~4 | .0256273 .0181474 1.41 0.158 -.0099653 .0612199 _Ihappines~5 | .0736566 .086237 0.85 0.393 -.0954801 .2427933 _IsexXhap_~2 | -.0088389 .0046613 -1.90 0.058 -.0179811 .0003032 _IsexXhap_~3 | -.0292948 .0114269 -2.56 0.010 -.0517063 -.0068833 _IsexXhap_~4 | -.0720886 .0224737 -3.21 0.001 -.1161663 -.0280108 _IsexXhap_~5 | -.1428534 .0978592 -1.46 0.145 -.3347848 .0490779 _cons | .9628054 .0016317 590.05 0.000 .9596051 .9660058 ------------------------------------------------------------------------------ 87 Logistic Regression • probability of success pi for the ith individual • vector of covariates xi associated with ith individual • dependent variable must be 0 or 1, independent variables xi can be categorical or continuous Does the probability of success pi depend on the covariates xi – and in what way? 88 Census Parameter Obtained from the logistic link function pi α βx i ln 1 pi and the census likelihood equation for the regression parameters Note: it is the log odds that is being modeled in terms of the covariate 89 Example: Ontario Health Survey How does the chance of suffering from hypertension depend on: • body mass index • age • gender • smoking habits • stress • a well-being score that is determined from selfperceived factors such as the energy one has, control over emotions, state of morale, interest in life and so on 90 STATA Commands use "I:\workshopjune\work.dta", clear svyset [pweight=indiv_wt], strata(newstrata) psu(ea) recode hyper (1=1) (2=0) (hyper: 24258 changes made) xi:svy: logit hyper bmi age i.sex i.smoktype i.stress i.wellbe i.sex _Isex_1-2 (naturally coded; _Isex_1 omitted) i.smoktype _Ismoktype_1-4 (naturally coded; _Ismoktype_1 omitted) i.stress _Istress_1-4 (naturally coded; _Istress_4 omitted) i.wellbe _Iwellbe_1-4 (naturally coded; _Iwellbe_1 omitted) (running logit on estimation sample) 91 STATA Output part I xi:svy: logit hyper bmi age i.sex i.smoktype i.stress i.wellbe i.sex _Isex_1-2 (naturally coded; _Isex_1 omitted) i.smoktype _Ismoktype_1-4 (naturally coded; _Ismoktype_1 omitted) i.stress _Istress_1-4 (naturally coded; _Istress_4 omitted) i.wellbe _Iwellbe_1-4 (naturally coded; _Iwellbe_1 omitted) (running logit on estimation sample) Number of strata Number of PSUs = = 72 1849 Number of obs Population size Design df F( 12, 1766) Prob > F = 25871 = 4341226.9 = 1777 = 64.99 = 0.0000 92 STAT Output part II -----------------------------------------------------------------------------| Linearized hyper | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------bmi | .1029348 .00803 12.82 0.000 .0871855 .118684 age | .0850085 .0040016 21.24 0.000 .0771601 .0928569 _Isex_2 | -.0094895 .0832978 -0.11 0.909 -.1728615 .1538825 _Ismoktype_2 | -.1068761 .100976 -1.06 0.290 -.3049203 .0911682 _Ismoktype_3 | -.1391754 .2245528 -0.62 0.535 -.5795907 .3012399 _Ismoktype_4 | -.1862018 .1050622 -1.77 0.077 -.3922601 .0198566 _Istress_1 | .4201336 .2115243 1.99 0.047 .005271 .8349961 _Istress_2 | .0103797 .2055384 0.05 0.960 -.3927428 .4135022 _Istress_3 | -.177385 .2015597 -0.88 0.379 -.572704 .217934 _Iwellbe_2 | -.6197166 .2755986 -2.25 0.025 -1.160248 -.0791852 _Iwellbe_3 | -.7841664 .2593617 -3.02 0.003 -1.292853 -.2754803 _Iwellbe_4 | -1.07929 .2600326 -4.15 0.000 -1.589292 -.5692879 _cons | -8.12002 .441972 -18.37 0.000 -8.98686 -7.25318 ------------------------------------------------------------------------------ 93 GEE: Generalized Estimating Equations Dependent or response variable • well-being measured on a 0 to 10 scale • focus is on women only Independent or explanatory variables’ • has responsibility for a child under age 12 (yes = 1, no = 2) • marital status (married = 1, separated = 2, divorced = 3, never married = 5 [widowed removed from the dataset]) • employment status (employed = 1, unemployed = 2, family care = 3) STATA syntax tsset pid year, yearly xi: xtgee wellbe i.mlstat i.job i.child i.sex [pweight = axrwght], family(poisson) link(identity) corr(exchangeable) 94 GEE Results -----------------------------------------------------------------------------| Semi-robust wellbe | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------_Imlstat_2 | 1.206905 .2036603 5.93 0.000 .8077382 1.606072 _Imlstat_3 | .3732488 .120658 3.09 0.002 .1367635 .6097342 _Imlstat_5 | -.0250266 .077469 -0.32 0.747 -.1768631 .1268098 _Ichild_2 | -.0456858 .063007 -0.73 0.468 -.1691773 .0778056 _Ijobc_2 | .9498503 .4045538 2.35 0.019 .1569394 1.742761 _Ijobc_3 | .0124392 .1827747 0.07 0.946 -.3457926 .370671 _cons | 1.922769 .0554797 34.66 0.000 1.814031 2.031507 ------------------------------------------------------------------------------ 95 For each type of initial marital status Married -----------------------------------------------------------------------------| Semi-robust wellbe | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------_Ichild_2 | .0666723 .0672237 0.99 0.321 -.0650836 .1984283 _Ijobc_2 | .888502 .720494 1.23 0.218 -.5236403 2.300644 _Ijobc_3 | .2989137 .2369747 1.26 0.207 -.1655482 .7633756 _cons | 1.825918 .0562928 32.44 0.000 1.715586 1.93625 ------------------------------------------------------------------------------ Separated or divorced -------------+---------------------------------------------------------------_Ichild_2 | -.6732289 .1847309 -3.64 0.000 -1.035295 -.3111629 _Ijobc_2 | 1.239189 .8163575 1.52 0.129 -.3608422 2.83922 _Ijobc_3 | -.2405778 .6582919 -0.37 0.715 -1.530806 1.049651 _cons | 2.777478 .1734716 16.01 0.000 2.43748 3.117476 ------------------------------------------------------------------------------ Never married -------------+---------------------------------------------------------------_Ichild_2 | -.5800375 .2041848 -2.84 0.005 -.9802324 -.1798426 _Ijobc_2 | .9851042 .5063179 1.95 0.052 -.0072607 1.977469 _Ijobc_3 | -.2799635 .290873 -0.96 0.336 -.8500642 .2901371 _cons | 2.406 .1951377 12.33 0.000 2.023538 2.788463 96 ------------------------------------------------------------------------------ Cox Proportional Hazards Model Dependent or outcome variable • time to breakdown of first marriage Independent or explanatory variables • gender • race (white/non-white) • Age in 1991 (restricted to 18 – 60) • financial position: comfortable=1, doing alright=2, just about getting by=3, quite difficult=4, very difficult =5 97 STATA Commands • Command for survival data set up stset tvariable [pweight = axrwght], failure(fail==1) scale(1) • Command for Cox proportional hazards mode xi: stcox i.sex i.arace aage i.afisit 98 STATA Output -----------------------------------------------------------------------------| Robust _t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------_Isex_2 | 1.251224 .1483865 1.89 0.059 .9917185 1.578635 _Iarace_1 | 1.979298 .7844764 1.72 0.085 .9102175 4.304047 aage | .9366 .0056464 -10.86 0.000 .9255984 .9477324 _Iafisit_2 | 1.226635 .201547 1.24 0.214 .8889056 1.692682 _Iafisit_3 | 1.519284 .2527755 2.51 0.012 1.096523 2.10504 _Iafisit_4 | 1.95182 .3985054 3.28 0.001 1.308124 2.912263 _Iafisit_5 | 1.936742 .5864388 2.18 0.029 1.069869 3.506006 ------------------------------------------------------------------------------ 99