1575:, who has argued that hidden bias may actually increase because matching on observed variables may unleash bias due to dormant unobserved confounders. Similarly, Pearl has argued that bias reduction can only be assured (asymptotically) by modelling the qualitative causal relationships between treatment, outcome, observed and unobserved covariates. Confounding occurs when the experimenter is unable to control for alternative, non-causal explanations for an observed relationship between independent and dependent variables. Such control should satisfy the "
5109:
4502:
102:. An observational study is required since it is unethical to randomly assign people to the treatment 'smoking.' The treatment effect estimated by simply comparing those who smoked to those who did not smoke would be biased by any factors that predict smoking (e.g.: gender and age). PSM attempts to control for these biases by making the groups receiving treatment and not-treatment comparable with respect to the control variables.
4488:
1629:: A dialog box for Propensity Score Matching is available from the IBM SPSS Statistics menu (Data/Propensity Score Matching), and allows the user to set the match tolerance, randomize case order when drawing samples, prioritize exact matches, sample with or without replacement, set a random seed, and maximize performance by increasing processing speed and minimizing memory usage.
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1567:
One disadvantage of PSM is that it only accounts for observed (and observable) covariates and not latent characteristics. Factors that affect assignment to treatment and outcome but that cannot be observed cannot be accounted for in the matching procedure. As the procedure only controls for observed
1547:
PSM has been shown to increase model "imbalance, inefficiency, model dependence, and bias," which is not the case with most other matching methods. The insights behind the use of matching still hold but should be applied with other matching methods; propensity scores also have other productive uses
94:
The "propensity" describes how likely a unit is to have been treated, given its covariate values. The stronger the confounding of treatment and covariates, and hence the stronger the bias in the analysis of the naive treatment effect, the better the covariates predict whether a unit is treated or
1555:
from observational data. The key advantages of PSM were, at the time of its introduction, that by using a linear combination of covariates for a single score, it balances treatment and control groups on a large number of covariates without losing a large number of observations. If units in the
218:
matching: same as radius matching, except control observations are weighted as a function of the distance between the treatment observation's propesnity score and control match propensity score. One example is the
Epanechnikov kernel. Radius matching is a special case where a uniform kernel is
118:
settings in which: (i) few units in the non-treatment comparison group are comparable to the treatment units; and (ii) selecting a subset of comparison units similar to the treatment unit is difficult because units must be compared across a high-dimensional set of pretreatment characteristics.
1538:
has shown that there exists a simple graphical test, called the back-door criterion, which detects the presence of confounding variables. To estimate the effect of treatment, the background variables X must block all back-door paths in the graph. This blocking can be done either by adding the
205:
Optimal full matching: match each participants to unique non-participant(s) so as to minimize the total distance in propensity scores between participants and their matched non-participants. This method can be combined with other matching
90:
attempts to reduce the treatment assignment bias, and mimic randomization, by creating a sample of units that received the treatment that is comparable on all observed covariates to a sample of units that did not receive the treatment.
122:
In normal matching, single characteristics that distinguish treatment and control groups are matched in an attempt to make the groups more alike. But if the two groups do not have substantial overlap, then substantial
1028:
209:
Caliper matching: comparison units within a certain width of the propensity score of the treated units get matched, where the width is generally a fraction of the standard deviation of the propensity score
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variables, any hidden bias due to latent variables may remain after matching. Another issue is that PSM requires large samples, with substantial overlap between treatment and control groups.
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82:, the randomization enables unbiased estimation of treatment effects; for each covariate, randomization implies that treatment-groups will be balanced on average, by the
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of a unit (e.g., person, classroom, school) being assigned to a particular treatment given a set of observed covariates. Propensity scores are used to reduce
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treatment and control were balanced on a large number of covariates one at a time, large numbers of observations would be needed to overcome the "
142:
PSM employs a predicted probability of group membershipâe.g., treatment versus control groupâbased on observed predictors, usually obtained from
941:
2161:
1896:
1871:
1741:
2070:"PSMATCH2: Stata module to perform full Mahalanobis and propensity score matching, common support graphing, and covariate imbalance testing"
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78:) between treated and untreated groups may be caused by a factor that predicts treatment rather than the treatment itself. In
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1560:" whereby the introduction of a new balancing covariate increases the minimum necessary number of observations in the sample
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1049:, or others), using some set of covariates. These propensity scores are then used as estimators for weights to be used with
260:
Use analyses appropriate for non-independent matched samples if more than one nonparticipant is matched to each participant
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For any value of a balancing score, the difference between the treatment and control means of the samples at hand (i.e.:
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may not include all (or any) of the ones used to decide on the treatment assignment. The numbering of the units (i.e.:
86:. Unfortunately, for observational studies, the assignment of treatments to research subjects is typically not random.
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Typically: a weighted mean of within-match average differences in outcomes between participants and non-participants.
1221:
1154:). The propensity score is the coarsest balancing score function, as it takes a (possibly) multidimensional object (
242:
3. Check that covariates are balanced across treatment and comparison groups within strata of the propensity score.
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variables that could be found in an estimate of the treatment effect obtained from simply comparing outcomes among
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not. By having units with similar propensity scores in both treatment and control, such confounding is reduced.
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2392:
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1969:
Hansen, Ben B; Klopfer, Stephanie Olsen (2006). "Optimal Full
Matching and Related Designs via Network Flows".
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1357:
758:
668:
346:
75:
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3471:
2173:"An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies"
685:
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2. Match each participant to one or more nonparticipants on propensity score, using one of these methods:
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Choose appropriate confounders (variables hypothesized to be associated with both treatment and outcome)
87:
79:
36:
5108:
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3391:
212:
Radius matching: all matches within a particular radius are used -- and reused between treatment units.
1918:"Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference"
5083:
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It is also strongly ignorable given any balancing function. Specifically, given the propensity score:
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40:
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confounding variable as a control in regression, or by matching on the confounding variable.
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The possibility of bias arises because a difference in the treatment outcome (such as the
4894:
1363:
352:
4542:
2119:(2006). "Large Sample Properties of Matching Estimators for Average Treatment Effects".
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2199:
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1602:
1163:) and transforms it into one dimension (although others, obviously, also exist), while
1046:
1692:"The Central Role of the Propensity Score in Observational Studies for Causal Effects"
1352:), based on subjects that have the same value of the balancing score, can serve as an
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2013:
1998:
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1615:: several commands implement propensity score matching, including the user-written
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1535:
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Any score that is 'finer' than the propensity score is a balancing score (i.e.:
1061:
The following were first presented, and proven, by
Rosenbaum and Rubin in 1983:
910:
906:
52:
249:
If covariates are not balanced, return to steps 1 or 2 and modify the procedure
43:
the effect of a treatment, policy, or other intervention by accounting for the
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2771:
2471:
2402:
2352:
2327:
2247:
1696:
1425:
Using sample estimates of balancing scores can produce sample balance on
663:
under control and treatment, respectively. Treatment assignment is said to be
151:
20:
1990:
1982:
1951:
1794:
1710:
1691:
3444:
3296:
2916:
2711:
2623:
2608:
2603:
2568:
1864:
Experimental and Quasi-experimental
Designs for Generalized Causal Inference
1830:
1576:
185:
44:
2208:
1848:
1457:. Furthermore, the above theorems indicate that the propensity score is a
531:
be a vector of observed pretreatment measurements (or covariates) for the
2960:
2578:
2455:
2450:
2445:
2417:
1936:
1917:
1785:
597:) are assumed to not contain any information beyond what is contained in
139:, which may make the comparison group look better or worse than reality.
1775:
1758:
1023:{\displaystyle e(x)\ {\stackrel {\mathrm {def} }{=}}\ \Pr(Z=1\mid X=x).}
4465:
4166:
178:= 0, if unit did not participate (i.e. is member of the control group).
1952:"MatchIt: Nonparametric Preprocessing for Parametric Causal Inference"
628:
index while still discussing the stochastic behavior of some subject.
4387:
3368:
3342:
3322:
2573:
2364:
235:
Difference-in-differences matching (kernel and local linear weights)
174:= 1, if unit participated (i.e. is member of the treatment group);
1612:
1531:
Graphical test for detecting the presence of confounding variables
127:
may be introduced. For example, if only the worst cases from the
47:
that predict receiving the treatment. PSM attempts to reduce the
2307:
1626:
4546:
4276:
3843:
3590:
2889:
2659:
2276:
2220:
246:
Use standardized differences or graphs to examine distributions
1619:. Stata version 13 and later also offers the built-in command
2216:
274:
The basic case is of two treatments (numbered 1 and 0), with
2052:
Implementing
Propensity Score Matching Estimators with STATA
562:
are made prior to treatment assignment, but the features in
1815:"Methods for Constructing and Assessing Propensity Scores"
2014:"Performing a 1:N Case-Control Match on Propensity Score"
1891:(Second ed.). New York: Cambridge University Press.
1591:: propensity score matching is available as part of the
1571:
General concerns with matching have also been raised by
279:
independent and identically distributed random variables
154:, alone or with other matching variables or covariates.
1759:"Why Propensity Scores Should Not Be Used for Matching"
1041:, propensity scores are estimated (via methods such as
1685:
1683:
1681:
1679:
1887:
Pearl, J. (2009). "Understanding propensity scores".
1862:
Shadish, W. R.; Cook, T. D.; Campbell, D. T. (2002).
1487:
1366:
1300:
1224:
1169:
1103:
1071:
944:
864:
817:
743:
688:
603:
568:
541:
510:
477:
444:
413:
355:
321:
291:
4129:
Autoregressive conditional heteroskedasticity (ARCH)
1201:
If treatment assignment is strongly ignorable given
5056:
5005:
4977:
4931:
4877:
4849:
4814:
4773:
4742:
4704:
4693:
4660:
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4142:
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3354:
3309:
3277:
3230:
3175:
3101:
3092:
2902:
2844:
2818:
2770:
2725:
2672:
2559:
2514:
2488:
2470:
2426:
2378:
2298:
2289:
1639:, a library for propensity score matching in python
1445:of the population that impacts the distribution of
150:. Propensity scores may be used for matching or as
1729:
1519:
1410:
1344:
1280:
1190:
1142:
1086:
1022:
885:
847:
749:
726:
616:
581:
554:
523:
496:
463:
426:
399:
337:
307:
1971:Journal of Computational and Graphical Statistics
1551:Like other matching procedures, PSM estimates an
987:
188:for the propensity score: predicted probability
61:received the treatment versus those that did not
3677:Multivariate adaptive regression splines (MARS)
1609:match observations based on a propensity score.
98:For example, one may be interested to know the
2088:"teffects psmatch â Propensity-score matching"
1281:{\displaystyle (r_{0},r_{1})\perp Z\mid e(X).}
913:by equating groups based on these covariates.
4558:
2232:
1690:Rosenbaum, Paul R.; Rubin, Donald B. (1983).
1345:{\displaystyle {\bar {r}}_{1}-{\bar {r}}_{0}}
646:(i.e.: conditionally unconfounded), and some
642:Let some subject have a vector of covariates
131:are compared to only the best cases from the
8:
1889:Causality: Models, Reasoning, and Inference
1757:King, Gary; Nielsen, Richard (2019-05-07).
1732:Causality: Models, Reasoning, and Inference
1548:in weighting and doubly robust estimation.
780:) is a function of the observed covariates
4701:
4565:
4551:
4543:
4286:
4273:
4190:
3996:
3865:
3840:
3611:
3587:
3315:
3098:
2899:
2886:
2669:
2656:
2295:
2286:
2273:
2239:
2225:
2217:
2154:Practical Propensity Score Methods using R
931:. The propensity score is defined as the
2198:
2134:
1935:
1838:
1784:
1774:
1709:
1508:
1495:
1486:
1399:
1377:
1365:
1336:
1325:
1324:
1314:
1303:
1302:
1299:
1245:
1232:
1223:
1168:
1102:
1070:
969:
968:
963:
961:
960:
943:
935:of treatment given background variables:
863:
816:
742:
706:
693:
687:
608:
602:
573:
567:
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509:
482:
476:
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418:
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366:
354:
326:
320:
296:
290:
162:1. Estimate propensity scores, e.g. with
1736:. New York: Cambridge University Press.
916:Suppose that we have a binary treatment
727:{\displaystyle r_{0},r_{1}\perp Z\mid X}
253:4. Estimate effects based on new sample
5074:Numerical smoothing and differentiation
1723:
1721:
1675:
632:Strongly ignorable treatment assignment
624:. The following sections will omit the
4203:KaplanâMeier estimator (product limit)
2030:
1583:Implementations in statistics packages
675:) conditional on background variables
345:. The quantity to be estimated is the
2156:. Washington, DC: Sage Publications.
1449:then the balancing score serves as a
927:, and background observed covariates
7:
4609:Iteratively reweighted least squares
4513:
4213:Accelerated failure time (AFT) model
679:. This can be written compactly as
285:would respond to the treatment with
4525:
3808:Analysis of variance (ANOVA, anova)
1605:: The PSMatch procedure, and macro
4627:Pearson product-moment correlation
3903:CochranâMantelâHaenszel statistics
2529:Pearson product-moment correlation
1977:(3). Informa UK Limited: 609â627.
1469:. Lastly, if treatment assignment
976:
973:
970:
848:{\displaystyle Z\perp X\mid b(X).}
71:introduced the technique in 1983.
14:
5107:
4524:
4512:
4500:
4487:
4486:
2178:Multivariate Behavioral Research
2171:Austin, Peter C. (31 May 2011).
2145:10.1111/j.1468-0262.2006.00655.x
1813:Garrido MM, et al. (2014).
535:th subject. The observations of
227:matching in conjunction with PSM
4162:Least-squares spectral analysis
2074:Statistical Software Components
1477:then the propensity score is a
593: = 1, ...,
3143:Mean-unbiased minimum-variance
1514:
1488:
1481:for the joint distribution of
1405:
1392:
1383:
1370:
1330:
1308:
1272:
1266:
1251:
1225:
1179:
1173:
1137:
1134:
1128:
1122:
1113:
1107:
1081:
1075:
1014:
990:
954:
948:
874:
868:
839:
833:
667:if the potential outcomes are
394:
381:
372:
359:
16:Statistical matching technique
1:
4456:Geographic information system
3672:Simultaneous equations models
1520:{\displaystyle (r_{0},r_{1})}
1051:Inverse probability weighting
858:The most trivial function is
804: = 1) and control (
5097:Regression analysis category
4987:Response surface methodology
3639:Coefficient of determination
3250:Uniformly most powerful test
2191:10.1080/00273171.2011.568786
1916:; Stuart, Elizabeth (2007).
1866:. Boston: Houghton Mifflin.
1803:(from the author's homepage)
1479:minimal sufficient statistic
1473:is strongly ignorable given
1459:minimal sufficient statistic
1437:If we think of the value of
1143:{\displaystyle e(X)=f(b(X))}
129:untreated "comparison" group
4969:FrischâWaughâLovell theorem
4939:Mean and predicted response
4208:Proportional hazards models
4152:Spectral density estimation
4134:Vector autoregression (VAR)
3568:Maximum posterior estimator
2800:Randomized controlled trial
1433:Relationship to sufficiency
800:) is the same for treated (
39:technique that attempts to
5176:
4619:Correlation and dependence
3968:Multivariate distributions
2388:Average absolute deviation
1912:Ho, Daniel; Imai, Kosuke;
635:
137:regression toward the mean
5092:
4964:Minimum mean-square error
4851:Decomposition of variance
4755:Growth curve (statistics)
4724:Generalized least squares
4482:
4285:
4272:
3956:Structural equation model
3864:
3839:
3610:
3586:
3318:
3292:Score/Lagrange multiplier
2898:
2885:
2707:Sample size determination
2668:
2655:
2285:
2272:
2254:
2152:Leite, Walter L. (2017).
201:Nearest neighbor matching
29:propensity score matching
4822:Generalized linear model
4714:Simple linear regression
4604:Non-linear least squares
4586:Computational statistics
4451:Environmental statistics
3973:Elliptical distributions
3766:Generalized linear model
3695:Simple linear regression
3465:HodgesâLehmann estimator
2922:Probability distribution
2831:Stochastic approximation
2393:Coefficient of variation
2037:: CS1 maint: location (
2019:. SUGI 29: SAS Institute
1983:10.1198/106186006x137047
1819:Health Services Research
1801:link to the full article
1553:average treatment effect
1358:average treatment effect
786:conditional distribution
759:statistical independence
347:average treatment effect
315:and to the control with
114:and confounding bias in
76:average treatment effect
4111:Cross-correlation (XCF)
3719:Non-standard predictors
3153:LehmannâScheffĂ© theorem
2826:Adaptive clinical trial
1831:10.1111/1475-6773.12182
933:conditional probability
808: = 0) units:
497:{\displaystyle Z_{i}=0}
464:{\displaystyle Z_{i}=1}
281:subjects. Each subject
231:Stratification matching
100:consequences of smoking
5114:Mathematics portal
5038:Orthogonal polynomials
4864:Analysis of covariance
4729:Weighted least squares
4719:Ordinary least squares
4670:Ordinary least squares
4507:Mathematics portal
4328:Engineering statistics
4236:NelsonâAalen estimator
3813:Analysis of covariance
3700:Ordinary least squares
3624:Pearson product-moment
3028:Statistical functional
2939:Empirical distribution
2772:Controlled experiments
2501:Frequency distribution
2279:Descriptive statistics
1711:10.1093/biomet/70.1.41
1558:dimensionality problem
1521:
1412:
1346:
1282:
1192:
1191:{\displaystyle b(X)=X}
1144:
1088:
1024:
923:, a response variable
887:
886:{\displaystyle b(X)=X}
849:
751:
750:{\displaystyle \perp }
728:
618:
583:
556:
525:
498:
465:
428:
401:
339:
338:{\displaystyle r_{0i}}
309:
308:{\displaystyle r_{1i}}
80:randomized experiments
5079:System identification
5043:Chebyshev polynomials
5028:Numerical integration
4979:Design of experiments
4923:Regression validation
4750:Polynomial regression
4675:Partial least squares
4423:Population statistics
4365:System identification
4099:Autocorrelation (ACF)
4027:Exponential smoothing
3941:Discriminant analysis
3936:Canonical correlation
3800:Partition of variance
3662:Regression validation
3506:(JonckheereâTerpstra)
3405:Likelihood-ratio test
3094:Frequentist inference
3006:Locationâscale family
2927:Sampling distribution
2892:Statistical inference
2859:Cross-sectional study
2846:Observational studies
2805:Randomized experiment
2634:Stem-and-leaf display
2436:Central limit theorem
1665:Matching (statistics)
1522:
1413:
1347:
1283:
1193:
1145:
1094:is a balancing score.
1089:
1065:The propensity score
1025:
888:
850:
752:
729:
619:
617:{\displaystyle X_{i}}
584:
582:{\displaystyle X_{i}}
557:
555:{\displaystyle X_{i}}
526:
524:{\displaystyle X_{i}}
499:
466:
434:indicates if subject
429:
427:{\displaystyle Z_{i}}
402:
340:
310:
192:or the log odds, log.
5084:Moving least squares
5023:Approximation theory
4959:Studentized residual
4949:Errors and residuals
4944:GaussâMarkov theorem
4859:Analysis of variance
4781:Nonlinear regression
4760:Segmented regression
4734:General linear model
4652:Confounding variable
4599:Linear least squares
4346:Probabilistic design
3931:Principal components
3774:Exponential families
3726:Nonlinear regression
3705:General linear model
3667:Mixed effects models
3657:Errors and residuals
3634:Confounding variable
3536:Bayesian probability
3514:Van der Waerden test
3504:Ordered alternative
3269:Multiple comparisons
3148:RaoâBlackwellization
3111:Estimating equations
3067:Statistical distance
2785:Factorial experiment
2318:Arithmetic-Geometric
2054:. Lecture notes 2001
1599:, or other packages.
1485:
1451:sufficient statistic
1364:
1298:
1222:
1167:
1101:
1087:{\displaystyle e(x)}
1069:
942:
862:
815:
741:
686:
601:
566:
539:
508:
475:
442:
411:
353:
319:
289:
170:Dependent variable:
148:counterfactual group
135:, the result may be
110:PSM is for cases of
84:law of large numbers
37:statistical matching
5155:Observational study
5145:Regression analysis
5102:Statistics category
5033:Gaussian quadrature
4918:Model specification
4885:Stepwise regression
4743:Predictor structure
4680:Total least squares
4662:Regression analysis
4647:Partial correlation
4578:regression analysis
4418:Official statistics
4341:Methods engineering
4022:Seasonal adjustment
3790:Poisson regressions
3710:Bayesian regression
3649:Regression analysis
3629:Partial correlation
3601:Regression analysis
3200:Prediction interval
3195:Likelihood interval
3185:Confidence interval
3177:Interval estimation
3138:Unbiased estimators
2956:Model specification
2836:Up-and-down designs
2524:Partial correlation
2480:Index of dispersion
2398:Interquartile range
1958:. 16 November 2022.
1776:10.1017/pan.2019.11
1411:{\displaystyle E-E}
1043:logistic regression
400:{\displaystyle E-E}
164:logistic regression
144:logistic regression
5119:Statistics outline
5018:Numerical analysis
4438:Spatial statistics
4318:Medical statistics
4218:First hitting time
4172:Whittle likelihood
3823:Degrees of freedom
3818:Multivariate ANOVA
3751:Heteroscedasticity
3563:Bayesian estimator
3528:Bayesian inference
3377:KolmogorovâSmirnov
3262:Randomization test
3232:Testing hypotheses
3205:Tolerance interval
3116:Maximum likelihood
3011:Exponential family
2944:Density estimation
2904:Statistical theory
2864:Natural experiment
2810:Scientific control
2727:Survey methodology
2413:Standard deviation
1937:10.1093/pan/mpl013
1923:Political Analysis
1763:Political Analysis
1728:Pearl, J. (2000).
1660:Heckman correction
1650:Rubin causal model
1577:backdoor criterion
1517:
1465:as a parameter of
1408:
1354:unbiased estimator
1342:
1278:
1198:is the finest one.
1188:
1150:for some function
1140:
1084:
1039:survey methodology
1033:In the context of
1020:
883:
845:
747:
724:
665:strongly ignorable
648:potential outcomes
614:
579:
552:
521:
494:
461:
424:
397:
335:
305:
265:Formal definitions
225:Mahalanobis metric
25:observational data
5132:
5131:
5124:Statistics topics
5069:Calibration curve
4878:Model exploration
4845:
4844:
4815:Non-normal errors
4706:Linear regression
4697:statistical model
4540:
4539:
4478:
4477:
4474:
4473:
4413:National accounts
4383:Actuarial science
4375:Social statistics
4268:
4267:
4264:
4263:
4260:
4259:
4195:Survival function
4180:
4179:
4042:Granger causality
3883:Contingency table
3858:Survival analysis
3835:
3834:
3831:
3830:
3687:Linear regression
3582:
3581:
3578:
3577:
3553:Credible interval
3522:
3521:
3305:
3304:
3121:Method of moments
2990:Parametric family
2951:Statistical model
2881:
2880:
2877:
2876:
2795:Random assignment
2717:Statistical power
2651:
2650:
2647:
2646:
2496:Contingency table
2466:
2465:
2333:Generalized/power
2163:978-1-4522-8888-8
1898:978-0-521-89560-6
1873:978-0-395-61556-0
1743:978-0-521-77362-1
1333:
1311:
986:
981:
959:
158:General procedure
65:Paul R. Rosenbaum
5167:
5160:Causal inference
5112:
5111:
4869:Multivariate AOV
4765:Local regression
4702:
4694:Regression as a
4685:Ridge regression
4632:Rank correlation
4567:
4560:
4553:
4544:
4528:
4527:
4516:
4515:
4505:
4504:
4490:
4489:
4393:Crime statistics
4287:
4274:
4191:
4157:Fourier analysis
4144:Frequency domain
4124:
4071:
4037:Structural break
3997:
3946:Cluster analysis
3893:Log-linear model
3866:
3841:
3782:
3756:Homoscedasticity
3612:
3588:
3507:
3499:
3491:
3490:(KruskalâWallis)
3475:
3460:
3415:Cross validation
3400:
3382:AndersonâDarling
3329:
3316:
3287:Likelihood-ratio
3279:Parametric tests
3257:Permutation test
3240:1- & 2-tails
3131:Minimum distance
3103:Point estimation
3099:
3050:Optimal decision
3001:
2900:
2887:
2869:Quasi-experiment
2819:Adaptive designs
2670:
2657:
2534:Rank correlation
2296:
2287:
2274:
2241:
2234:
2227:
2218:
2212:
2202:
2167:
2148:
2138:
2117:Imbens, Guido W.
2099:
2098:
2092:
2084:
2078:
2077:
2061:
2055:
2049:
2043:
2042:
2036:
2028:
2026:
2024:
2018:
2009:
2003:
2002:
1966:
1960:
1959:
1948:
1942:
1941:
1939:
1909:
1903:
1902:
1884:
1878:
1877:
1859:
1853:
1852:
1842:
1810:
1804:
1798:
1788:
1778:
1754:
1748:
1747:
1735:
1725:
1716:
1715:
1713:
1687:
1638:
1622:
1621:teffects psmatch
1618:
1608:
1598:
1594:
1526:
1524:
1523:
1518:
1513:
1512:
1500:
1499:
1417:
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1409:
1404:
1403:
1382:
1381:
1351:
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1340:
1335:
1334:
1326:
1319:
1318:
1313:
1312:
1304:
1287:
1285:
1284:
1279:
1250:
1249:
1237:
1236:
1197:
1195:
1194:
1189:
1149:
1147:
1146:
1141:
1093:
1091:
1090:
1085:
1035:causal inference
1029:
1027:
1026:
1021:
984:
983:
982:
980:
979:
967:
962:
957:
903:propensity score
897:Propensity score
892:
890:
889:
884:
854:
852:
851:
846:
756:
754:
753:
748:
733:
731:
730:
725:
711:
710:
698:
697:
623:
621:
620:
615:
613:
612:
588:
586:
585:
580:
578:
577:
561:
559:
558:
553:
551:
550:
530:
528:
527:
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520:
519:
503:
501:
500:
495:
487:
486:
470:
468:
467:
462:
454:
453:
433:
431:
430:
425:
423:
422:
406:
404:
403:
398:
393:
392:
371:
370:
344:
342:
341:
336:
334:
333:
314:
312:
311:
306:
304:
303:
116:non-experimental
112:causal inference
5175:
5174:
5170:
5169:
5168:
5166:
5165:
5164:
5135:
5134:
5133:
5128:
5106:
5088:
5052:
5048:Chebyshev nodes
5001:
4997:Bayesian design
4973:
4954:Goodness of fit
4927:
4900:
4890:Model selection
4873:
4841:
4810:
4769:
4738:
4695:
4689:
4656:
4613:
4580:
4571:
4541:
4536:
4499:
4470:
4432:
4369:
4355:quality control
4322:
4304:Clinical trials
4281:
4256:
4240:
4228:Hazard function
4222:
4176:
4138:
4122:
4085:
4081:BreuschâGodfrey
4069:
4046:
3986:
3961:Factor analysis
3907:
3888:Graphical model
3860:
3827:
3794:
3780:
3760:
3714:
3681:
3643:
3606:
3605:
3574:
3518:
3505:
3497:
3489:
3473:
3458:
3437:Rank statistics
3431:
3410:Model selection
3398:
3356:Goodness of fit
3350:
3327:
3301:
3273:
3226:
3171:
3160:Median unbiased
3088:
2999:
2932:Order statistic
2894:
2873:
2840:
2814:
2766:
2721:
2664:
2662:Data collection
2643:
2555:
2510:
2484:
2462:
2422:
2374:
2291:Continuous data
2281:
2268:
2250:
2245:
2215:
2170:
2164:
2151:
2136:10.1.1.559.6313
2113:Abadie, Alberto
2111:
2107:
2102:
2090:
2086:
2085:
2081:
2063:
2062:
2058:
2050:
2046:
2029:
2022:
2020:
2016:
2012:Parsons, Lori.
2011:
2010:
2006:
1968:
1967:
1963:
1950:
1949:
1945:
1911:
1910:
1906:
1899:
1886:
1885:
1881:
1874:
1861:
1860:
1856:
1812:
1811:
1807:
1756:
1755:
1751:
1744:
1727:
1726:
1719:
1689:
1688:
1677:
1673:
1646:
1636:
1620:
1616:
1606:
1596:
1592:
1585:
1545:
1533:
1504:
1491:
1483:
1482:
1461:if thinking of
1435:
1395:
1373:
1362:
1361:
1323:
1301:
1296:
1295:
1241:
1228:
1220:
1219:
1165:
1164:
1162:
1099:
1098:
1067:
1066:
1059:
940:
939:
899:
860:
859:
813:
812:
771:balancing score
767:
765:Balancing score
739:
738:
702:
689:
684:
683:
662:
655:
640:
634:
604:
599:
598:
569:
564:
563:
542:
537:
536:
511:
506:
505:
478:
473:
472:
445:
440:
439:
438:got treatment (
414:
409:
408:
407:. The variable
384:
362:
351:
350:
322:
317:
316:
292:
287:
286:
272:
267:
160:
133:treatment group
108:
17:
12:
11:
5:
5173:
5171:
5163:
5162:
5157:
5152:
5147:
5137:
5136:
5130:
5129:
5127:
5126:
5121:
5116:
5104:
5099:
5093:
5090:
5089:
5087:
5086:
5081:
5076:
5071:
5066:
5060:
5058:
5054:
5053:
5051:
5050:
5045:
5040:
5035:
5030:
5025:
5020:
5014:
5012:
5003:
5002:
5000:
4999:
4994:
4992:Optimal design
4989:
4983:
4981:
4975:
4974:
4972:
4971:
4966:
4961:
4956:
4951:
4946:
4941:
4935:
4933:
4929:
4928:
4926:
4925:
4920:
4915:
4914:
4913:
4908:
4903:
4898:
4887:
4881:
4879:
4875:
4874:
4872:
4871:
4866:
4861:
4855:
4853:
4847:
4846:
4843:
4842:
4840:
4839:
4834:
4829:
4824:
4818:
4816:
4812:
4811:
4809:
4808:
4803:
4798:
4793:
4791:Semiparametric
4788:
4783:
4777:
4775:
4771:
4770:
4768:
4767:
4762:
4757:
4752:
4746:
4744:
4740:
4739:
4737:
4736:
4731:
4726:
4721:
4716:
4710:
4708:
4699:
4691:
4690:
4688:
4687:
4682:
4677:
4672:
4666:
4664:
4658:
4657:
4655:
4654:
4649:
4644:
4638:
4636:Spearman's rho
4629:
4623:
4621:
4615:
4614:
4612:
4611:
4606:
4601:
4596:
4590:
4588:
4582:
4581:
4572:
4570:
4569:
4562:
4555:
4547:
4538:
4537:
4535:
4534:
4522:
4510:
4496:
4483:
4480:
4479:
4476:
4475:
4472:
4471:
4469:
4468:
4463:
4458:
4453:
4448:
4442:
4440:
4434:
4433:
4431:
4430:
4425:
4420:
4415:
4410:
4405:
4400:
4395:
4390:
4385:
4379:
4377:
4371:
4370:
4368:
4367:
4362:
4357:
4348:
4343:
4338:
4332:
4330:
4324:
4323:
4321:
4320:
4315:
4310:
4301:
4299:Bioinformatics
4295:
4293:
4283:
4282:
4277:
4270:
4269:
4266:
4265:
4262:
4261:
4258:
4257:
4255:
4254:
4248:
4246:
4242:
4241:
4239:
4238:
4232:
4230:
4224:
4223:
4221:
4220:
4215:
4210:
4205:
4199:
4197:
4188:
4182:
4181:
4178:
4177:
4175:
4174:
4169:
4164:
4159:
4154:
4148:
4146:
4140:
4139:
4137:
4136:
4131:
4126:
4118:
4113:
4108:
4107:
4106:
4104:partial (PACF)
4095:
4093:
4087:
4086:
4084:
4083:
4078:
4073:
4065:
4060:
4054:
4052:
4051:Specific tests
4048:
4047:
4045:
4044:
4039:
4034:
4029:
4024:
4019:
4014:
4009:
4003:
4001:
3994:
3988:
3987:
3985:
3984:
3983:
3982:
3981:
3980:
3965:
3964:
3963:
3953:
3951:Classification
3948:
3943:
3938:
3933:
3928:
3923:
3917:
3915:
3909:
3908:
3906:
3905:
3900:
3898:McNemar's test
3895:
3890:
3885:
3880:
3874:
3872:
3862:
3861:
3844:
3837:
3836:
3833:
3832:
3829:
3828:
3826:
3825:
3820:
3815:
3810:
3804:
3802:
3796:
3795:
3793:
3792:
3776:
3770:
3768:
3762:
3761:
3759:
3758:
3753:
3748:
3743:
3738:
3736:Semiparametric
3733:
3728:
3722:
3720:
3716:
3715:
3713:
3712:
3707:
3702:
3697:
3691:
3689:
3683:
3682:
3680:
3679:
3674:
3669:
3664:
3659:
3653:
3651:
3645:
3644:
3642:
3641:
3636:
3631:
3626:
3620:
3618:
3608:
3607:
3604:
3603:
3598:
3592:
3591:
3584:
3583:
3580:
3579:
3576:
3575:
3573:
3572:
3571:
3570:
3560:
3555:
3550:
3549:
3548:
3543:
3532:
3530:
3524:
3523:
3520:
3519:
3517:
3516:
3511:
3510:
3509:
3501:
3493:
3477:
3474:(MannâWhitney)
3469:
3468:
3467:
3454:
3453:
3452:
3441:
3439:
3433:
3432:
3430:
3429:
3428:
3427:
3422:
3417:
3407:
3402:
3399:(ShapiroâWilk)
3394:
3389:
3384:
3379:
3374:
3366:
3360:
3358:
3352:
3351:
3349:
3348:
3340:
3331:
3319:
3313:
3311:Specific tests
3307:
3306:
3303:
3302:
3300:
3299:
3294:
3289:
3283:
3281:
3275:
3274:
3272:
3271:
3266:
3265:
3264:
3254:
3253:
3252:
3242:
3236:
3234:
3228:
3227:
3225:
3224:
3223:
3222:
3217:
3207:
3202:
3197:
3192:
3187:
3181:
3179:
3173:
3172:
3170:
3169:
3164:
3163:
3162:
3157:
3156:
3155:
3150:
3135:
3134:
3133:
3128:
3123:
3118:
3107:
3105:
3096:
3090:
3089:
3087:
3086:
3081:
3076:
3075:
3074:
3064:
3059:
3058:
3057:
3047:
3046:
3045:
3040:
3035:
3025:
3020:
3015:
3014:
3013:
3008:
3003:
2987:
2986:
2985:
2980:
2975:
2965:
2964:
2963:
2958:
2948:
2947:
2946:
2936:
2935:
2934:
2924:
2919:
2914:
2908:
2906:
2896:
2895:
2890:
2883:
2882:
2879:
2878:
2875:
2874:
2872:
2871:
2866:
2861:
2856:
2850:
2848:
2842:
2841:
2839:
2838:
2833:
2828:
2822:
2820:
2816:
2815:
2813:
2812:
2807:
2802:
2797:
2792:
2787:
2782:
2776:
2774:
2768:
2767:
2765:
2764:
2762:Standard error
2759:
2754:
2749:
2748:
2747:
2742:
2731:
2729:
2723:
2722:
2720:
2719:
2714:
2709:
2704:
2699:
2694:
2692:Optimal design
2689:
2684:
2678:
2676:
2666:
2665:
2660:
2653:
2652:
2649:
2648:
2645:
2644:
2642:
2641:
2636:
2631:
2626:
2621:
2616:
2611:
2606:
2601:
2596:
2591:
2586:
2581:
2576:
2571:
2565:
2563:
2557:
2556:
2554:
2553:
2548:
2547:
2546:
2541:
2531:
2526:
2520:
2518:
2512:
2511:
2509:
2508:
2503:
2498:
2492:
2490:
2489:Summary tables
2486:
2485:
2483:
2482:
2476:
2474:
2468:
2467:
2464:
2463:
2461:
2460:
2459:
2458:
2453:
2448:
2438:
2432:
2430:
2424:
2423:
2421:
2420:
2415:
2410:
2405:
2400:
2395:
2390:
2384:
2382:
2376:
2375:
2373:
2372:
2367:
2362:
2361:
2360:
2355:
2350:
2345:
2340:
2335:
2330:
2325:
2323:Contraharmonic
2320:
2315:
2304:
2302:
2293:
2283:
2282:
2277:
2270:
2269:
2267:
2266:
2261:
2255:
2252:
2251:
2246:
2244:
2243:
2236:
2229:
2221:
2214:
2213:
2185:(3): 399â424.
2168:
2162:
2149:
2129:(1): 235â267.
2108:
2106:
2103:
2101:
2100:
2079:
2056:
2044:
2004:
1961:
1943:
1930:(3): 199â236.
1904:
1897:
1879:
1872:
1854:
1825:(5): 1701â20.
1805:
1769:(4): 435â454.
1749:
1742:
1717:
1674:
1672:
1669:
1668:
1667:
1662:
1657:
1652:
1645:
1642:
1641:
1640:
1630:
1624:
1610:
1600:
1584:
1581:
1544:
1541:
1532:
1529:
1516:
1511:
1507:
1503:
1498:
1494:
1490:
1434:
1431:
1430:
1429:
1422:
1421:
1420:
1419:
1407:
1402:
1398:
1394:
1391:
1388:
1385:
1380:
1376:
1372:
1369:
1339:
1332:
1329:
1322:
1317:
1310:
1307:
1291:
1290:
1289:
1288:
1277:
1274:
1271:
1268:
1265:
1262:
1259:
1256:
1253:
1248:
1244:
1240:
1235:
1231:
1227:
1214:
1213:
1207:
1206:
1199:
1187:
1184:
1181:
1178:
1175:
1172:
1158:
1139:
1136:
1133:
1130:
1127:
1124:
1121:
1118:
1115:
1112:
1109:
1106:
1095:
1083:
1080:
1077:
1074:
1058:
1055:
1047:random forests
1031:
1030:
1019:
1016:
1013:
1010:
1007:
1004:
1001:
998:
995:
992:
989:
978:
975:
972:
966:
956:
953:
950:
947:
898:
895:
882:
879:
876:
873:
870:
867:
856:
855:
844:
841:
838:
835:
832:
829:
826:
823:
820:
784:such that the
766:
763:
746:
735:
734:
723:
720:
717:
714:
709:
705:
701:
696:
692:
671:of treatment (
660:
653:
633:
630:
611:
607:
576:
572:
549:
545:
518:
514:
493:
490:
485:
481:
471:) or control (
460:
457:
452:
448:
421:
417:
396:
391:
387:
383:
380:
377:
374:
369:
365:
361:
358:
332:
329:
325:
302:
299:
295:
271:
270:Basic settings
268:
266:
263:
262:
261:
258:
251:
250:
247:
240:
239:
238:Exact matching
236:
233:
228:
221:
220:
213:
210:
207:
203:
194:
193:
182:
179:
159:
156:
107:
104:
15:
13:
10:
9:
6:
4:
3:
2:
5172:
5161:
5158:
5156:
5153:
5151:
5148:
5146:
5143:
5142:
5140:
5125:
5122:
5120:
5117:
5115:
5110:
5105:
5103:
5100:
5098:
5095:
5094:
5091:
5085:
5082:
5080:
5077:
5075:
5072:
5070:
5067:
5065:
5064:Curve fitting
5062:
5061:
5059:
5055:
5049:
5046:
5044:
5041:
5039:
5036:
5034:
5031:
5029:
5026:
5024:
5021:
5019:
5016:
5015:
5013:
5011:
5010:approximation
5008:
5004:
4998:
4995:
4993:
4990:
4988:
4985:
4984:
4982:
4980:
4976:
4970:
4967:
4965:
4962:
4960:
4957:
4955:
4952:
4950:
4947:
4945:
4942:
4940:
4937:
4936:
4934:
4930:
4924:
4921:
4919:
4916:
4912:
4909:
4907:
4904:
4902:
4901:
4893:
4892:
4891:
4888:
4886:
4883:
4882:
4880:
4876:
4870:
4867:
4865:
4862:
4860:
4857:
4856:
4854:
4852:
4848:
4838:
4835:
4833:
4830:
4828:
4825:
4823:
4820:
4819:
4817:
4813:
4807:
4804:
4802:
4799:
4797:
4794:
4792:
4789:
4787:
4786:Nonparametric
4784:
4782:
4779:
4778:
4776:
4772:
4766:
4763:
4761:
4758:
4756:
4753:
4751:
4748:
4747:
4745:
4741:
4735:
4732:
4730:
4727:
4725:
4722:
4720:
4717:
4715:
4712:
4711:
4709:
4707:
4703:
4700:
4698:
4692:
4686:
4683:
4681:
4678:
4676:
4673:
4671:
4668:
4667:
4665:
4663:
4659:
4653:
4650:
4648:
4645:
4642:
4641:Kendall's tau
4639:
4637:
4633:
4630:
4628:
4625:
4624:
4622:
4620:
4616:
4610:
4607:
4605:
4602:
4600:
4597:
4595:
4594:Least squares
4592:
4591:
4589:
4587:
4583:
4579:
4575:
4574:Least squares
4568:
4563:
4561:
4556:
4554:
4549:
4548:
4545:
4533:
4532:
4523:
4521:
4520:
4511:
4509:
4508:
4503:
4497:
4495:
4494:
4485:
4484:
4481:
4467:
4464:
4462:
4461:Geostatistics
4459:
4457:
4454:
4452:
4449:
4447:
4444:
4443:
4441:
4439:
4435:
4429:
4428:Psychometrics
4426:
4424:
4421:
4419:
4416:
4414:
4411:
4409:
4406:
4404:
4401:
4399:
4396:
4394:
4391:
4389:
4386:
4384:
4381:
4380:
4378:
4376:
4372:
4366:
4363:
4361:
4358:
4356:
4352:
4349:
4347:
4344:
4342:
4339:
4337:
4334:
4333:
4331:
4329:
4325:
4319:
4316:
4314:
4311:
4309:
4305:
4302:
4300:
4297:
4296:
4294:
4292:
4291:Biostatistics
4288:
4284:
4280:
4275:
4271:
4253:
4252:Log-rank test
4250:
4249:
4247:
4243:
4237:
4234:
4233:
4231:
4229:
4225:
4219:
4216:
4214:
4211:
4209:
4206:
4204:
4201:
4200:
4198:
4196:
4192:
4189:
4187:
4183:
4173:
4170:
4168:
4165:
4163:
4160:
4158:
4155:
4153:
4150:
4149:
4147:
4145:
4141:
4135:
4132:
4130:
4127:
4125:
4123:(BoxâJenkins)
4119:
4117:
4114:
4112:
4109:
4105:
4102:
4101:
4100:
4097:
4096:
4094:
4092:
4088:
4082:
4079:
4077:
4076:DurbinâWatson
4074:
4072:
4066:
4064:
4061:
4059:
4058:DickeyâFuller
4056:
4055:
4053:
4049:
4043:
4040:
4038:
4035:
4033:
4032:Cointegration
4030:
4028:
4025:
4023:
4020:
4018:
4015:
4013:
4010:
4008:
4007:Decomposition
4005:
4004:
4002:
3998:
3995:
3993:
3989:
3979:
3976:
3975:
3974:
3971:
3970:
3969:
3966:
3962:
3959:
3958:
3957:
3954:
3952:
3949:
3947:
3944:
3942:
3939:
3937:
3934:
3932:
3929:
3927:
3924:
3922:
3919:
3918:
3916:
3914:
3910:
3904:
3901:
3899:
3896:
3894:
3891:
3889:
3886:
3884:
3881:
3879:
3878:Cohen's kappa
3876:
3875:
3873:
3871:
3867:
3863:
3859:
3855:
3851:
3847:
3842:
3838:
3824:
3821:
3819:
3816:
3814:
3811:
3809:
3806:
3805:
3803:
3801:
3797:
3791:
3787:
3783:
3777:
3775:
3772:
3771:
3769:
3767:
3763:
3757:
3754:
3752:
3749:
3747:
3744:
3742:
3739:
3737:
3734:
3732:
3731:Nonparametric
3729:
3727:
3724:
3723:
3721:
3717:
3711:
3708:
3706:
3703:
3701:
3698:
3696:
3693:
3692:
3690:
3688:
3684:
3678:
3675:
3673:
3670:
3668:
3665:
3663:
3660:
3658:
3655:
3654:
3652:
3650:
3646:
3640:
3637:
3635:
3632:
3630:
3627:
3625:
3622:
3621:
3619:
3617:
3613:
3609:
3602:
3599:
3597:
3594:
3593:
3589:
3585:
3569:
3566:
3565:
3564:
3561:
3559:
3556:
3554:
3551:
3547:
3544:
3542:
3539:
3538:
3537:
3534:
3533:
3531:
3529:
3525:
3515:
3512:
3508:
3502:
3500:
3494:
3492:
3486:
3485:
3484:
3481:
3480:Nonparametric
3478:
3476:
3470:
3466:
3463:
3462:
3461:
3455:
3451:
3450:Sample median
3448:
3447:
3446:
3443:
3442:
3440:
3438:
3434:
3426:
3423:
3421:
3418:
3416:
3413:
3412:
3411:
3408:
3406:
3403:
3401:
3395:
3393:
3390:
3388:
3385:
3383:
3380:
3378:
3375:
3373:
3371:
3367:
3365:
3362:
3361:
3359:
3357:
3353:
3347:
3345:
3341:
3339:
3337:
3332:
3330:
3325:
3321:
3320:
3317:
3314:
3312:
3308:
3298:
3295:
3293:
3290:
3288:
3285:
3284:
3282:
3280:
3276:
3270:
3267:
3263:
3260:
3259:
3258:
3255:
3251:
3248:
3247:
3246:
3243:
3241:
3238:
3237:
3235:
3233:
3229:
3221:
3218:
3216:
3213:
3212:
3211:
3208:
3206:
3203:
3201:
3198:
3196:
3193:
3191:
3188:
3186:
3183:
3182:
3180:
3178:
3174:
3168:
3165:
3161:
3158:
3154:
3151:
3149:
3146:
3145:
3144:
3141:
3140:
3139:
3136:
3132:
3129:
3127:
3124:
3122:
3119:
3117:
3114:
3113:
3112:
3109:
3108:
3106:
3104:
3100:
3097:
3095:
3091:
3085:
3082:
3080:
3077:
3073:
3070:
3069:
3068:
3065:
3063:
3060:
3056:
3055:loss function
3053:
3052:
3051:
3048:
3044:
3041:
3039:
3036:
3034:
3031:
3030:
3029:
3026:
3024:
3021:
3019:
3016:
3012:
3009:
3007:
3004:
3002:
2996:
2993:
2992:
2991:
2988:
2984:
2981:
2979:
2976:
2974:
2971:
2970:
2969:
2966:
2962:
2959:
2957:
2954:
2953:
2952:
2949:
2945:
2942:
2941:
2940:
2937:
2933:
2930:
2929:
2928:
2925:
2923:
2920:
2918:
2915:
2913:
2910:
2909:
2907:
2905:
2901:
2897:
2893:
2888:
2884:
2870:
2867:
2865:
2862:
2860:
2857:
2855:
2852:
2851:
2849:
2847:
2843:
2837:
2834:
2832:
2829:
2827:
2824:
2823:
2821:
2817:
2811:
2808:
2806:
2803:
2801:
2798:
2796:
2793:
2791:
2788:
2786:
2783:
2781:
2778:
2777:
2775:
2773:
2769:
2763:
2760:
2758:
2757:Questionnaire
2755:
2753:
2750:
2746:
2743:
2741:
2738:
2737:
2736:
2733:
2732:
2730:
2728:
2724:
2718:
2715:
2713:
2710:
2708:
2705:
2703:
2700:
2698:
2695:
2693:
2690:
2688:
2685:
2683:
2680:
2679:
2677:
2675:
2671:
2667:
2663:
2658:
2654:
2640:
2637:
2635:
2632:
2630:
2627:
2625:
2622:
2620:
2617:
2615:
2612:
2610:
2607:
2605:
2602:
2600:
2597:
2595:
2592:
2590:
2587:
2585:
2584:Control chart
2582:
2580:
2577:
2575:
2572:
2570:
2567:
2566:
2564:
2562:
2558:
2552:
2549:
2545:
2542:
2540:
2537:
2536:
2535:
2532:
2530:
2527:
2525:
2522:
2521:
2519:
2517:
2513:
2507:
2504:
2502:
2499:
2497:
2494:
2493:
2491:
2487:
2481:
2478:
2477:
2475:
2473:
2469:
2457:
2454:
2452:
2449:
2447:
2444:
2443:
2442:
2439:
2437:
2434:
2433:
2431:
2429:
2425:
2419:
2416:
2414:
2411:
2409:
2406:
2404:
2401:
2399:
2396:
2394:
2391:
2389:
2386:
2385:
2383:
2381:
2377:
2371:
2368:
2366:
2363:
2359:
2356:
2354:
2351:
2349:
2346:
2344:
2341:
2339:
2336:
2334:
2331:
2329:
2326:
2324:
2321:
2319:
2316:
2314:
2311:
2310:
2309:
2306:
2305:
2303:
2301:
2297:
2294:
2292:
2288:
2284:
2280:
2275:
2271:
2265:
2262:
2260:
2257:
2256:
2253:
2249:
2242:
2237:
2235:
2230:
2228:
2223:
2222:
2219:
2210:
2206:
2201:
2196:
2192:
2188:
2184:
2180:
2179:
2174:
2169:
2165:
2159:
2155:
2150:
2146:
2142:
2137:
2132:
2128:
2124:
2123:
2118:
2114:
2110:
2109:
2104:
2096:
2089:
2083:
2080:
2075:
2071:
2067:
2060:
2057:
2053:
2048:
2045:
2040:
2034:
2015:
2008:
2005:
2000:
1996:
1992:
1988:
1984:
1980:
1976:
1972:
1965:
1962:
1957:
1953:
1947:
1944:
1938:
1933:
1929:
1925:
1924:
1919:
1915:
1908:
1905:
1900:
1894:
1890:
1883:
1880:
1875:
1869:
1865:
1858:
1855:
1850:
1846:
1841:
1836:
1832:
1828:
1824:
1820:
1816:
1809:
1806:
1802:
1796:
1792:
1787:
1786:1721.1/128459
1782:
1777:
1772:
1768:
1764:
1760:
1753:
1750:
1745:
1739:
1734:
1733:
1724:
1722:
1718:
1712:
1707:
1703:
1699:
1698:
1693:
1686:
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1682:
1680:
1676:
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1653:
1651:
1648:
1647:
1643:
1634:
1631:
1628:
1625:
1614:
1611:
1607:OneToManyMTCH
1604:
1601:
1590:
1587:
1586:
1582:
1580:
1578:
1574:
1569:
1565:
1563:
1562:geometrically
1559:
1554:
1549:
1543:Disadvantages
1542:
1540:
1537:
1530:
1528:
1509:
1505:
1501:
1496:
1492:
1480:
1476:
1472:
1468:
1464:
1460:
1456:
1452:
1448:
1444:
1440:
1432:
1428:
1424:
1423:
1400:
1396:
1389:
1386:
1378:
1374:
1367:
1359:
1355:
1337:
1327:
1320:
1315:
1305:
1293:
1292:
1275:
1269:
1263:
1260:
1257:
1254:
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1238:
1233:
1229:
1218:
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1211:
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1208:
1204:
1200:
1185:
1182:
1176:
1170:
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1157:
1153:
1131:
1125:
1119:
1116:
1110:
1104:
1096:
1078:
1072:
1064:
1063:
1062:
1057:Main theorems
1056:
1054:
1052:
1048:
1044:
1040:
1036:
1017:
1011:
1008:
1005:
1002:
999:
996:
993:
964:
951:
945:
938:
937:
936:
934:
930:
926:
922:
919:
914:
912:
908:
904:
896:
894:
880:
877:
871:
865:
842:
836:
830:
827:
824:
821:
818:
811:
810:
809:
807:
803:
799:
795:
791:
787:
783:
779:
775:
772:
764:
762:
760:
744:
721:
718:
715:
712:
707:
703:
699:
694:
690:
682:
681:
680:
678:
674:
670:
666:
659:
652:
649:
645:
639:
631:
629:
627:
609:
605:
596:
592:
574:
570:
547:
543:
534:
516:
512:
491:
488:
483:
479:
458:
455:
450:
446:
437:
419:
415:
389:
385:
378:
375:
367:
363:
356:
348:
330:
327:
323:
300:
297:
293:
284:
280:
277:
269:
264:
259:
256:
255:
254:
248:
245:
244:
243:
237:
234:
232:
229:
226:
223:
222:
217:
214:
211:
208:
204:
202:
199:
198:
197:
191:
187:
183:
180:
177:
173:
169:
168:
167:
165:
157:
155:
153:
149:
145:
140:
138:
134:
130:
126:
120:
117:
113:
105:
103:
101:
96:
92:
89:
85:
81:
77:
72:
70:
66:
62:
58:
54:
50:
46:
42:
38:
34:
30:
26:
22:
5150:Epidemiology
5057:Applications
4896:
4774:Non-standard
4529:
4517:
4498:
4491:
4403:Econometrics
4353: /
4336:Chemometrics
4313:Epidemiology
4306: /
4279:Applications
4121:ARIMA model
4068:Q-statistic
4017:Stationarity
3913:Multivariate
3856: /
3852: /
3850:Multivariate
3848: /
3788: /
3784: /
3558:Bayes factor
3457:Signed rank
3369:
3343:
3335:
3323:
3018:Completeness
2854:Cohort study
2752:Opinion poll
2687:Missing data
2674:Study design
2629:Scatter plot
2551:Scatter plot
2544:Spearman's Ï
2506:Grouped data
2182:
2176:
2153:
2126:
2122:Econometrica
2120:
2105:Bibliography
2095:Stata Manual
2094:
2082:
2073:
2064:Leuven, E.;
2059:
2047:
2021:. Retrieved
2007:
1974:
1970:
1964:
1955:
1946:
1927:
1921:
1907:
1888:
1882:
1863:
1857:
1822:
1818:
1808:
1766:
1762:
1752:
1731:
1704:(1): 41â55.
1701:
1695:
1655:Ignorability
1579:" of Pearl.
1570:
1566:
1550:
1546:
1534:
1474:
1470:
1466:
1462:
1454:
1446:
1438:
1436:
1426:
1202:
1159:
1155:
1151:
1060:
1032:
928:
924:
920:
915:
902:
900:
857:
805:
801:
797:
793:
789:
781:
777:
773:
770:
768:
736:
676:
672:
664:
657:
650:
647:
643:
641:
638:Ignorability
625:
594:
590:
532:
435:
282:
275:
273:
252:
241:
195:
189:
175:
171:
161:
146:to create a
141:
121:
109:
97:
93:
73:
69:Donald Rubin
32:
28:
23:analysis of
18:
4531:WikiProject
4446:Cartography
4408:Jurimetrics
4360:Reliability
4091:Time domain
4070:(LjungâBox)
3992:Time-series
3870:Categorical
3854:Time-series
3846:Categorical
3781:(Bernoulli)
3616:Correlation
3596:Correlation
3392:JarqueâBera
3364:Chi-squared
3126:M-estimator
3079:Asymptotics
3023:Sufficiency
2790:Interaction
2702:Replication
2682:Effect size
2639:Violin plot
2619:Radar chart
2599:Forest plot
2589:Correlogram
2539:Kendall's Ï
2066:Sianesi, B.
1573:Judea Pearl
1536:Judea Pearl
911:confounding
907:probability
669:independent
206:techniques.
53:confounding
21:statistical
5139:Categories
4932:Background
4895:Mallows's
4398:Demography
4116:ARMA model
3921:Regression
3498:(Friedman)
3459:(Wilcoxon)
3397:Normality
3387:Lilliefors
3334:Student's
3210:Resampling
3084:Robustness
3072:divergence
3062:Efficiency
3000:(monotone)
2995:Likelihood
2912:Population
2745:Stratified
2697:Population
2516:Dependence
2472:Count data
2403:Percentile
2380:Dispersion
2313:Arithmetic
2248:Statistics
1914:King, Gary
1697:Biometrika
1671:References
636:See also:
186:estimation
184:Obtain an
152:covariates
45:covariates
5007:Numerical
3779:Logistic
3546:posterior
3472:Rank sum
3220:Jackknife
3215:Bootstrap
3033:Bootstrap
2968:Parameter
2917:Statistic
2712:Statistic
2624:Run chart
2609:Pie chart
2604:Histogram
2594:Fan chart
2569:Bar chart
2451:L-moments
2338:Geometric
2131:CiteSeerX
1991:1061-8600
1956:R Project
1795:1047-1987
1443:parameter
1387:−
1331:¯
1321:−
1309:¯
1261:∣
1255:⊥
1053:methods.
1003:∣
918:indicator
828:∣
822:⊥
745:⊥
719:∣
713:⊥
376:−
4837:Logistic
4827:Binomial
4806:Isotonic
4801:Quantile
4493:Category
4186:Survival
4063:Johansen
3786:Binomial
3741:Isotonic
3328:(normal)
2973:location
2780:Blocking
2735:Sampling
2614:QâQ plot
2579:Box plot
2561:Graphics
2456:Skewness
2446:Kurtosis
2418:Variance
2348:Heronian
2343:Harmonic
2209:21818162
2068:(2003).
2033:cite web
2023:June 10,
1999:10138048
1849:24779867
1644:See also
1617:psmatch2
1597:optmatch
757:denotes
106:Overview
88:Matching
41:estimate
4832:Poisson
4519:Commons
4466:Kriging
4351:Process
4308:studies
4167:Wavelet
4000:General
3167:Plug-in
2961:L space
2740:Cluster
2441:Moments
2259:Outline
2200:3144483
1840:4213057
1593:MatchIt
1356:of the
905:is the
504:). Let
51:due to
35:) is a
19:In the
4796:Robust
4388:Census
3978:Normal
3926:Manova
3746:Robust
3496:2-way
3488:1-way
3326:-test
2997:
2574:Biplot
2365:Median
2358:Lehmer
2300:Center
2207:
2197:
2160:
2133:
1997:
1989:
1895:
1870:
1847:
1837:
1793:
1740:
1633:Python
985:
958:
792:given
737:where
216:Kernel
4012:Trend
3541:prior
3483:anova
3372:-test
3346:-test
3338:-test
3245:Power
3190:Pivot
2983:shape
2978:scale
2428:Shape
2408:Range
2353:Heinz
2328:Cubic
2264:Index
2091:(PDF)
2017:(PDF)
1995:S2CID
1637:PsmPy
1613:Stata
1441:as a
1205:then:
219:used.
125:error
59:that
57:units
4576:and
4245:Test
3445:Sign
3297:Wald
2370:Mode
2308:Mean
2205:PMID
2158:ISBN
2039:link
2025:2016
1987:ISSN
1893:ISBN
1868:ISBN
1845:PMID
1791:ISSN
1738:ISBN
1627:SPSS
1453:for
1037:and
656:and
67:and
49:bias
4911:BIC
4906:AIC
3425:BIC
3420:AIC
2195:PMC
2187:doi
2141:doi
1979:doi
1932:doi
1835:PMC
1827:doi
1781:hdl
1771:doi
1706:doi
1603:SAS
788:of
33:PSM
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1700:.
1694:.
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1045:,
988:Pr
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1471:Z
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1406:]
1401:0
1397:r
1393:[
1390:E
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1379:1
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1270:X
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1234:0
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1180:)
1177:X
1174:(
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