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docs/source/glossary.rst

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A notation for describing statistical models :footcite:p:`wilkinson1973symbolic`.
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References
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----------
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.. footbibliography::
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Glossary
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========
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.. glossary::
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:sorted:
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ANCOVA
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Analysis of covariance is a simple linear model, typically with one continuous predictor (the covariate) and a catgeorical variable (which may correspond to treatment or control group). In the context of this package, ANCOVA could be useful in pre-post treatment designs, either with or without random assignment. This is similar to the approach of difference in differences, but only applicable with a single pre and post treatment measure.
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Average treatment effect
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ATE
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The average treatement effect across all units.
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Average treatment effect on the treated
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ATT
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The average effect of the treatment on the units that recieved it. Also called Treatment on the treated.
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Change score analysis
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A statistical procedure where the outcome variable is the difference between the posttest and protest scores.
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Comparative interrupted time-series
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CITS
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An interrupted time series design with added comparison time series observations.
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Confound
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Anything besides the treatment which varies across the treatment and control conditions.
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Counterfactual
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A hypothetical outcome that could or will occur under specific hypothetical circumstances.
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Difference in differences
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DiD
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Analysis where the treatment effect is estimated as a difference between treatment conditions in the differences between pre-treatment to post treatment observations.
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Interrupted time series design
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ITS
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A quasi-experimental design to estimate a treatment effect where a series of observations are collected before and after a treatment. No control group is present.
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Non-equivalent group designs
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NEGD
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A quasi-experimental design where units are assigned to conditions non-randomly, and not according to a running variable (see Regression discontinuity design).
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One-group posttest-only design
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A design where a single group is exposed to a treatment and assessed on an outcome measure. There is no pretest measure or comparison group.
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Panel data
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Time series data collected on multiple units where the same units are observed at each time point.
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Pretest-posttest design
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A quasi-experimental design where the treatment effect is estimated by comparing an outcome measure before and after treatment.
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Quasi-experiment
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An empirical comparison used to estimate the effects of a treatment where units are not assigned to conditions at random.
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Random assignment
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Where units are assigned to conditions at random.
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Randomized experiment
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An emprical comparison used to estimate the effects of treatments where units are assigned to treatment conditions randomly.
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Regression discontinuity design
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A quasi–experimental comparison to estimate a treatment effect where units are assigned to treatment conditions based on a cut-off score on a quantitative assignment variable (aka running variable).
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Sharp regression discontinuity design
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A Regression discontinuity design where allocation to treatment or control is determined by a sharp threshold / step function.
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Synthetic control
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The synthetic control method is a statistical method used to evaluate the effect of an intervention in comparative case studies. It involves the construction of a weighted combination of groups used as controls, to which the treatment group is compared.
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Treatment on the treated effect
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TOT
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The average effect of the treatment on the units that recieved it. Also called the average treatment effect on the treated (ATT).
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Treatment effect
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The difference in outcomes between what happened after a treatment is implemented and what would have happened (see Counterfactual) if the treatment had not been implemented, assuming everything else had been the same.
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Wilkinson notation
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A notation for describing statistical models :footcite:p:`wilkinson1973symbolic`.
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References
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----------
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.. footbibliography::

docs/source/notebooks/did_pymc_banks.ipynb

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"source": [
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"# Banking dataset with a `pymc` model\n",
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"\n",
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":::{note}\n",
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"This example is in-progress! Further elaboration and explanation will follow soon.\n",
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":::\n",
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"\n",
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"This notebook analyses historic data on banking closures from [Richardson & Troost (2009)](http://masteringmetrics.com/wp-content/uploads/2015/02/Richardson_Troost_2009_JPE.pdf) and used as a case study for a difference in differences analysis in the [Mastering Metrics](http://www.masteringmetrics.com) book. Here, we replicate this analysis, but using Bayesian inference."
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"This notebook analyses historic data on banking closures from {cite:t}`richardson2009monetary` and used as a case study for a difference in differences analysis in the excellent book [Mastering Metrics](http://www.masteringmetrics.com) {cite:p}`angrist2014mastering`. Here, we replicate this analysis, but using Bayesian inference."
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]
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},
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"The only change here compared to the classic 2$\\times$2 DiD model above is the addition of a main effect of `year`. Because this is coded numerically (not categorically) this can capture any linear changes in the outcome variable over time."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We will use the formula: `bib ~ 1 + year + district*post_treatment` which equates to the following model of expected values:\n",
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"\n",
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"$$\n",
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"\\begin{aligned}\n",
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"\\mu_i & = \\beta_0 \\\\\n",
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" & \\quad + \\beta_{y} \\cdot year_i \\\\\n",
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" & \\quad + \\beta_{d} \\cdot district_i \\\\\n",
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" & \\quad + \\beta_{p} \\cdot post~treatment_i \\\\\n",
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" & \\quad + \\beta_{\\Delta} \\cdot district_i \\cdot post~treatment_i\n",
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"\\end{aligned}\n",
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"$$\n",
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"\n",
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"The only change here compared to the classic 2$\\times$2 DiD model above is the addition of a main effect of `year`. Because this is coded numerically (not categorically) this can capture any linear changes in the outcome variable over time."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,

docs/source/references.bib

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publisher={American Economic Association}
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}
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@book{hansenEconometrics,
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title={Econometrics},
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author={Hansen, Bruce E},
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year={2022},
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publisher={Princeton}
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}
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@online{brexit2022policybrief,
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year={2022},
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title={What can we know about the cost of Brexit so far?},
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url={https://www.cer.eu/publications/archive/policy-brief/2022/cost-brexit-so-far},
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author={Springford, John}
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}
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@book{reichardt2019quasi,
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title={Quasi-experimentation: A guide to design and analysis},
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author={Reichardt, Charles S},
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year={2019},
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publisher={Guilford Publications}
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}
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@article{wilkinson1973symbolic,
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title={Symbolic description of factorial models for analysis of variance},
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author={Wilkinson, GN and Rogers, CE},
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journal={Journal of the Royal Statistical Society Series C: Applied Statistics},
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volume={22},
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number={3},
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pages={392--399},
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year={1973},
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publisher={Oxford University Press}
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}
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@article{wilkinson1973symbolic,
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title={Symbolic description of factorial models for analysis of variance},
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author={Wilkinson, GN and Rogers, CE},

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