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Some approximations of the logistic distribution with application to the covariance matrix of logistic regression
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
2014 (English)In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 85, 63-68 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we show that a two-component normal mixture model provides a good approximation to the logistic distribution. This approximation is an improvement over using the normal distribution and is comparable to using the t-distribution as approximating distributions. The results from using the mixture model is exemplified by finding an approximative analytic expression for the covariance matrix of logistic regression using normally distributed random regressors.

Place, publisher, year, edition, pages
2014. Vol. 85, 63-68 p.
Keyword [en]
Density, Gaussian, Mixture, Normal, t -distribution
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:uu:diva-221566DOI: 10.1016/j.spl.2013.11.007ISI: 000331665000009OAI: oai:DiVA.org:uu-221566DiVA: diva2:709472
Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Some Aspects of Propensity Score-based Estimators for Causal Inference
Open this publication in new window or tab >>Some Aspects of Propensity Score-based Estimators for Causal Inference
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of four papers that are related to commonly used propensity score-based estimators for average causal effects.

The first paper starts with the observation that researchers often have access to data containing lots of covariates that are correlated. We therefore study the effect of correlation on the asymptotic variance of an inverse probability weighting and a matching estimator. Under the assumptions of normally distributed covariates, constant causal effect, and potential outcomes and a logit that are linear in the parameters we show that the correlation influences the asymptotic efficiency of the estimators differently, both with regard to direction and magnitude. Further, the strength of the confounding towards the outcome and the treatment plays an important role.

The second paper extends the first paper in that the estimators are studied under the more realistic setting of using the estimated propensity score. We also relax several assumptions made in the first paper, and include the doubly robust estimator. Again, the results show that the correlation may increase or decrease the variances of the estimators, but we also observe that several aspects influence how correlation affects the variance of the estimators, such as the choice of estimator, the strength of the confounding towards the outcome and the treatment, and whether constant or non-constant causal effect is present.

The third paper concerns estimation of the asymptotic variance of a propensity score matching estimator. Simulations show that large gains can be made for the mean squared error by properly selecting smoothing parameters of the variance estimator and that a residual-based local linear estimator may be a more efficient estimator for the asymptotic variance. The specification of the variance estimator is shown to be crucial when evaluating the effect of right heart catheterisation, i.e. we show either a negative effect on survival or no significant effect depending on the choice of smoothing parameters.  

In the fourth paper, we provide an analytic expression for the covariance matrix of logistic regression with normally distributed regressors. This paper is related to the other papers in that logistic regression is commonly used to estimate the propensity score.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2014. 24 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 99
Keyword
correlation, treatment effect, inverse probability weighting, local linear estimator, matching, multicollinearity, observational study.
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-229341 (URN)978-91-554-8990-8 (ISBN)
Public defence
2014-09-19, Hörsal 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2014-08-29 Created: 2014-08-06 Last updated: 2014-09-08

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Publisher's full texthttp://www.sciencedirect.com/science/article/pii/S016771521300388X

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Pingel, Ronnie

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