The silhouette width is one of the very popular choices when it comes to selecting the optimal number of clusters. It measures the similarity of each point to its cluster, and compares that to the similarity of the point with the closest neighboring cluster. This metric ranges between -1 to 1, where a higher value implies better similarity of the points to their clusters.

library(cluster)gower_df <- daisy(german_credit_clean, metric = "gower" , type = list(logratio = 2))

  mutate_if(is.character, as.factor)

We find that the variable amount needs a log transformation due to the positive skew in its distribution.

e details about the mathematics of Gower distance are quite complicated and left out for another article.

Clustering datasets having both numerical and categorical variables

For each observation iii, calculate the average dissimilarity aiaia_i between iii and all other points of the cluster to which i belongs. For all other clusters CCC, to which i does not belong, calculate the average dissimilarity d(i,C)d(i,C)d(i, C) of iii to all observations of C. The smallest of these d(i,C)d(i,C)d(i,C) is defined as bi=minCd(i,C)bi=minCd(i,C)b_i= \min_C d(i,C). The value of bibib_i can be seen as the dissimilarity between iii and its “neighbor” cluster, i.e., the nearest one to which it does not belong. Finally the silhouette width of the observation iii is defined by the formula: Si=(bi−ai)/max(ai,bi)Si=(bi−ai)/max(ai,bi)S_i = (b_i - a_i)/max(a_i, b_i).

Average silhouette method

The total WSS measures the compactness of the clustering and we want it to be as small as possible.

To avoid distortions caused by excessive outliers, it’s possible to use PAM algorithm, which is less sensitive to outliers.

Next, the wss (within sum of square) is drawn according to the number of clusters. The location of a bend (knee) in the plot is generally considered as an indicator of the appropriate number of clusters.

K-means algorithm can be summarized as follow: Specify the number of clusters (K) to be created (by the analyst) Select randomly k objects from the dataset as the initial cluster centers or means Assigns each observation to their closest centroid, based on the Euclidean distance between the object and the centroid For each of the k clusters update the cluster centroid by calculating the new mean values of all the data points in the cluster. The centoid of a Kth cluster is a vector of length p containing the means of all variables for the observations in the kth cluster; p is the number of variables. Iteratively minimize the total within sum of square. That is, iterate steps 3 and 4 until the cluster assignments stop changing or the maximum number of iterations is reached. By default, the R software uses 10 as the default value for the maximum number of iterations.

to use correlation distance, the data are input as z-scores.

A successful evaluation of discriminant validity shows that a test of a concept is not highly correlated with other tests designed to measure theoretically different concepts.

The remaining term, 1 / (1 − Rj2) is the VIF. It reflects all other factors that influence the uncertainty in the coefficient estimates. The VIF equals 1 when the vector Xj is orthogonal to each column of the design matrix for the regression of Xj on the other covariates. By contrast, the VIF is greater than 1 when the vector Xj is not orthogonal to all columns of the design matrix for the regression of Xj on the other covariates. Finally, note that the VIF is invariant to the scaling of the variables

It turns out that the square of this standard error, the estimated variance of the estimate of βj, can be equivalently expressed as:[3][4] var ^ ( β ^ j ) = s 2 ( n − 1 ) var ^ ( X j ) ⋅ 1 1 − R j 2 , {\displaystyle {\widehat {\operatorname {var} }}({\hat {\beta }}_{j})={\frac {s^{2}}{(n-1){\widehat {\operatorname {var} }}(X_{j})}}\cdot {\frac {1}{1-R_{j}^{2}}},} where Rj2 is the multiple R2 for the regression of Xj on the other covariates (a regression that does not involve the response variable Y). This identity separates the influences of several distinct factors on the variance of the coefficient estimate: s2: greater scatter in the data around the regression surface leads to proportionately more variance in the coefficient estimates n: greater sample size results in proportionately less variance in the coefficient estimates var ^ ( X j ) {\displaystyle {\widehat {\operatorname {var} }}(X_{j})} : greater variability in a particular covariate leads to proportionately less variance in the corresponding coefficient estimate The remaining term, 1 / (1 − Rj2) is the VIF. It reflects all other factors that influence the uncertainty in the coefficient estimates

Summary: Algorithms to Live By

When treatment assign-ment takes place in waves, it is natural to adapt Thompson sampling by assigning a non-random numberpdtNtof observations in wavetto treatmentd, in order to reduce ran-domness. The remainder of observations are assigned randomly so that expected sharesremain equal topdt.

Q = 12 n k ( k + 1 ) ∑ j = 1 k ( r ¯ ⋅ j − k + 1 2 ) 2 {\displaystyle Q={\frac {12n}{k(k+1)}}\sum _{j=1}^{k}\left({\bar {r}}_{\cdot j}-{\frac {k+1}{2}}\right)^{2}} . Note

is the rank of x i j {\displaystyle x_{ij}}

Find the values r ¯ ⋅ j = 1 n ∑ i = 1 n r i j {\displaystyle {\bar {r}}_{\cdot j}={\frac {1}{n}}\sum _{i=1}^{n}{r_{ij}}}

Definitions

Individual donors, governments and firms demonstrate substantial generosity (e.g., UK charity represents 0.5-1% of GDP, US charity around 2% of GDP).

how people react to the presentation of charity-effectiveness information.

Beem101: Project, discussion of research

pure’ altruism or ‘warm glow’ altruism (Andreoni 1990; Ashraf and Bandiera 2017)

The Global Priorities Institute’s vision and mission

Formula[edit] The Y-intercept of the SML is equal to the risk-free interest rate. The slope of the SML is equal to the market risk premium and reflects the risk return tradeoff at a given time: S M L : E ( R i ) = R f + β i [ E ( R M ) − R f ] {\displaystyle \mathrm {SML} :E(R_{i})=R_{f}+\beta _{i}[E(R_{M})-R_{f}]\,} where: E(Ri) is an expected return on security E(RM) is an expected return on market portfolio M β is a nondiversifiable or systematic risk RM is a market rate of return Rf is a risk-free rate

The Y-intercept of the SML is equal to the risk-free interest rate. The slope of the SML is equal to the market risk premium and reflects the risk return tradeoff at a given time: S M L : E ( R i ) = R f + β i [ E ( R M ) − R f ] {\displaystyle \mathrm {SML} :E(R_{i})=R_{f}+\beta _{i}[E(R_{M})-R_{f}]\,} where: E(Ri) is an expected return on security E(RM) is an expected return on market portfolio M β is a nondiversifiable or systematic risk RM is a market rate of return Rf is a risk-free rate

This abnormal extra return above the market's return at a given level of risk is what is called the alpha.

Capital asset pricing model

quantity beta (β)

systematic risk (beta) t

If the fraction q {\displaystyle q} of a one-unit (e.g. one-million-dollar) portfolio is placed in asset X and the fraction 1 − q {\displaystyle 1-q} is placed in Y, the stochastic portfolio return is q x + ( 1 − q ) y {\displaystyle qx+(1-q)y} . If x {\displaystyle x} and y {\displaystyle y} are uncorrelated, the variance of portfolio return is var ( q x + ( 1 − q ) y ) = q 2 σ x 2 + ( 1 − q ) 2 σ y 2 {\displaystyle {\text{var}}(qx+(1-q)y)=q^{2}\sigma _{x}^{2}+(1-q)^{2}\sigma _{y}^{2}} . The variance-minimizing value of q {\displaystyle q} is q = σ y 2 / [ σ x 2 + σ y 2 ] {\displaystyle q=\sigma _{y}^{2}/[\sigma _{x}^{2}+\sigma _{y}^{2}]} , which is strictly between 0 {\displaystyle 0} and 1 {\displaystyle 1} . Using this value of q {\displaystyle q} in the expression for the variance of portfolio return gives the latter as σ x 2 σ y 2 / [ σ x 2 + σ y 2 ] {\displaystyle \sigma _{x}^{2}\sigma _{y}^{2}/[\sigma _{x}^{2}+\sigma _{y}^{2}]} , which is less than what it would be at either of the undiversified values q = 1 {\displaystyle q=1} and q = 0 {\displaystyle q=0} (which respectively give portfolio return variance of σ x 2 {\displaystyle \sigma _{x}^{2}} and σ y 2 {\displaystyle \sigma _{y}^{2}} ). Note that the favorable effect of diversification on portfolio variance would be enhanced if x {\displaystyle x} and y {\displaystyle y} were negatively correlated but diminished (though not eliminated) if they were positively correlated.

Similarly, a 1985 book reported that most value from diversification comes from the first 15 or 20 different stocks in a portfolio.[6]

d(p)=(209000-130p)

CLV Formula

“Sue’s mother” RaRaR_a “Sue’s lecturer in the UK” →→\rightarrow false (so it’s not ‘transitive’)

intend

(Highly optional): Properties of binary relations - O-R problem 1a.

Students

We say that uu is ’a utility function for ≿\succsim.

Differentiating this wrt III yields Engel aggregation:

direct

Past Projects

That's because cause prioritization research is extremely difficult, not because no one has thought to do this.

4. It is difficult to find cause neutral funding.I think funders like to choose their cause and stick with it so there is a lack of cause neutral funding. 

Growth and the case against randomista development,

me that when reading the GPI research agenda, the economics parts read like it was written by philosophers.

(Also, I have never worked in academia so there may be theories of change in the academic space that others could identify.)

But for a new organisation to solely focus on doing the research that they believed would be most useful for improving the world it is unclear what the theory of change would be.

I think that people are hesitant to do something new if they think it is being done, and funders want to know why the new thing is different so the abundance of organisations that used to do cause prioritisation research or do research that is a subcategory of cause prioritisation research limits other organisations from starting up.

Theoretical cause selection beyond speculation. Evidence of how to reason well despite uncertainty and more comparisons of different causes.

more consideration of second order effect

Let me give just one example, if you look at best practice in risk assessment methodologies[5] it looks very different from the naive expected value calculations used in EA

theorists

e. From my point of view, I could save a human life for ~£3000. I don’t want to let kids die needlessly if I can stop it. I personally think that the future is really important but before I drop the ball on all the things I know will have an impact it would be nice to have:

(There could be experimental hits based giving.)

Now let’s get a bit more complicated and do some more research and find other interventions and consider long run effects and so on”. There could be research looking for strong empirical evidence into:the second order or long run effects of existing interventions.how to drive economic growth, policy change, structural changes, and so forth.

Looking around it feels a like there is a split down the middle of the EA community:[4] On the one hand you have the empiricals: those who believe that doing good is difficult, common sense leads you astray and to create change we need hard data, ideally at least a few RCTs.On the other side are the theorists: those who believe you just need to think really hard and to choose a cause we need expected value calculations and it matters not if calculations are highly uncertain if the numbers tend to infinity.Personally I find myself somewhat drawn to the uncharted middle ground.

Post community building I moved back into policy and most recently have found myself in the policy space, building support for future generations in the UK Parliament. Not research. Not waiting. But creating change.

The case of the missing cause prioritisation research

We theoretically expect and empirically observe impact to be “heavy tailed” with some causes being orders of magnitude more impactful

Students: please propose some of these as a Hypothes.is comment HERE.

well

How individuals interact with one another, and the consequences of this (Game theory and mechanism design/agency problems)

This relies heavily on:

We’re backed by Open Philanthropy, Effective Altruism Funds, and viewers like you.

In typical meta-analyses, we do not have the individual data for each participant available, but only the aggregated effects, which is why we have to perform meta-regressions with predictors on a study level

Same is the case once we detect statistical heterogeneity in our fixed-effect-model meta-analysis, as indicated by

A useful statistic for quantifying inconsistency is , where Q is the chi-squared statistic and df is its degrees of freedom (Higgins 2002, Higgins 2003). This describes the percentage of the variability in effect estimates that is due to heterogeneity rather than sampling error (chance).  

MODELS IN MICROECONOMIC THEORY

wasting

We can use the ecdf function to implement the ECDF in R, and then check the probability of our pooled effect being smaller than 0.30. The code looks like this.

We see that the posterior distributions follow a unimodal, and roughly normal distribution, peaking around the values for μμ\mu and ττ\tau we saw in the output.

By using the ranef function, we can also extract the estimated deviation of each study’s “true” effect size from the pooled effect: ranef(m.brm) ## $Author ## , , Intercept ## ## Estimate Est.Error Q2.5 Q97.5 ## Call et al. 0.07181028

0.09

Please be aware that Bayesian methods are much more computationally intensive compared to the standard meta-analytic techniques we covered before; it may therefore take a few minutes until the sampling is completed.

m.brm <- brm(TE|se(seTE) ~ 1 + (1|Author), data = ThirdWave, prior = priors, iter = 4000)

In this example, I will use my ThirdWave dataset, which contains data of a real-world meta-analysis investigating the effects of “Third-Wave” psychotherapies in college students. The data is identical to the madata dataset we used in Chapter 4.

using a sophisticated algorithm

call2() is often convenient to program with,

lobstr::ast(f1(f2(a, b), f3(1, f4(2))))

f <- expr(f(x = 1, y = 2)) # Add a new argument f$z <- 3 f #> f(x = 1, y = 2, z = 3)

function specifically designed to capture user input in a function argument: enexpr()

expr() lets you capture code that you’ve typed

Note that when you attach another package with library(), the parent environment of the global environment changes:

Unlike lists, setting an element to NULL does not remove it, because sometimes you want a name that refers to NULL. Instead, use env_unbind():

But you can’t use [[ with numeric indices, and you can’t use [:

Only one environment doesn’t have a parent: the empty environment.

The current environment, or current_env() is the environment in which code is currently executing. When you’re experimenting interactively, that’s usually the global environment, or global_env(). The global environment is sometimes called your “workspace”, as it’s where all interactive (i.e. outside of a function) computation takes place.

env_print() which gives us a little more information:

e1$d <- e1

Advanced R

Replication is testing the same claims using data that was not used in the original study. That required some changes from us. Starting in Round 6, Replication Markets will no longer distinguish between “data replication” and “direct replication.” 

t has been argued that a good approach is to use weakly informative priors (Williams, Rast, and Bürkner 2018). Weaky informative priors can be contrasted with non-informative priors.

integrate prior knowledge and assumptions when calculating meta-analyses.

It can either be stored as the raw data (including the Mean, N, and SD of every study arm) Or it only contains the calculated effect sizes and the standard error (SE).

meta and metafor package which do most of the heavy lifting, there are still some aspects of meta-analyses in the biomedical field and psychology which we consider important, but are not easy to do in R currently, particularly if you do not have a programming or statistics background. To fill this gap, we developed the dmetar package, which serves as the companion R package for this guide. The dmetar package has its own documentation, which can be found here. Functions of the dmetar package provide additional functionality for the meta and metafor packages (and a few other, more advanced packages), w

set_variable_labels(s1 = "Sex", s2 = "Yes or No?")

preview_chapter()

Error in files2[[format]] : 
  attempt to select less than one element in get1index

But if you end up with a very long series of chained if statements, you should consider rewriting. One useful technique is the switch() function. It allows you to evaluate selected code based on position or name. #> function(x, y, op) { #> switch(op, #> plus = x + y, #> minus = x - y, #> times = x * y, #> divide = x / y, #> stop("Unknown op!") #> ) #> }

The second type of tutorial provides much richer feedback and assessment, but also requires considerably more effort to author. If you are primarily interested in this sort of tutorial, there are many features in learnr to support it, including exercise hints and solutions, automated exercise checkers, and multiple choice quizzes with custom feedback.

There are two main types of tutorial documents: Tutorials that are mostly narrative and/or video content, and also include some runnable code chunks. These documents are very similar to package vignettes in that their principal goal is communicating concepts. The interactive tutorial features are then used to allow further experimentation by the reader. Tutorials that provide a structured learning experience with multiple exercises, quiz questions, and tailored feedback. The first type of tutorial is much easier to author while still being very useful. These documents will typically add exercise = TRUE to selected code chunks, and also set exercise.eval = TRUE so the chunk output is visible by default. The reader can simply look at the R code and move on, or play with it to reinforce their understanding.

button “Run Document” in RStudio, or call the function rmarkdown::run() on this Rmd file

image conscience donors

First, many health experts, including the surgeon general of the United States, told the public simultaneously that masks weren’t necessary for protecting the general public and that health care workers needed the dwindling supply. This contradiction confuses an ordinary listener. How do these masks magically protect the wearers only and only if they work in a particular field?

These results arein line with predictions, such that in those cases in which aconsequentialist judgment does not clearly violate fairness-basedprinciples about respecting others and not treating them as meremeans, people do not infer that the agent is necessarily an untrust-worthy social partner

We reasoned that if deontological agents are preferred overconsequentialist agents because they are perceived as more com-mitted to social cooperation, such preferences should be lessenedif consequentialist agents reported their judgments as being verydifficult to make, indicating some level of commitment to coop-eration (Critcher, Inbar, & Pizarro, 2013). From the process dis-sociation perspective (Conway & Gawronski, 2013), a person whoreports that it is easy to make a characteristically consequentialistjudgment can be interpreted as being high in consequentialism

In contrast to the previous studies, for the switch dilemma,consequentialist agents were rated to be no less moral (Z0.73,p.47,d0.10) or trustworthy (Z1.87,p.06,d0.26)than deontological agents.

. Despite thegeneral endorsement many people have that “ends do not justifymeans,” people do typically judge that sacrificing the one man bydiverting the train is less morally wrong than sacrificing the manby using his body to stop the train (Foot, 1967; Greene et al.,2001).

The switch case differs from the footbridge case in two criticalways

The only difference is thatAdam does not push the large man, but instead pushes a button thatopens a trapdoor that causes the large man to fall onto the tracks.

The amount of moneyparticipants transferred to the agent (from $0.00 to $0.30) was usedas an indicator of trustworthiness, as was how much money theybelieved they would receive back from the agent (0% to 100%)

. However, the data did not support a meresimilarity effect: Our results were robust to controlling for partic-ipants’ own moral judgments, such that participants who made adeontological judgment (the majority) strongly preferred a deon-tological agent, whereas participants who made a consequentialistjudgment (the minority) showed no preference between the two

However, the central claims behind thisaccount—that people who express deontological moral intuitions areperceived as more trustworthy and favored as cooperation partners—has not been empirically investigated.

the typicaldeontological reason for why specific actions are wrong is that theyviolate duties to respect persons and honor social obligations—fea-tures that are crucial when selecting a social partner. An individualwho claims that stealing is always morally wrong and believes them-selves morally obligated to act in accordance with this duty seemsmuch less likely to steal from me than an individual who believes thatthe stealing is sometimes morally acceptable depending on the con-sequences. Actors who express characteristically deontological judg-ments may therefore be preferred to those expressing consequentialistjudgments because these judgments may be more reliable indicatorsof stable cooperative behavior.

First, deontologists’ prohibition of certain acts or behaviors mayserve as a relevant cue for inferring trustworthiness, because theextent to which someone claims to follow rule or action-based judg-ments may be associated with the reliability of their moral behavior.One piece of preliminary evidence for this comes from a studyshowing that agents willing to punish third parties who violate fair-ness principles are trusted more, and actually are more trustworthy(Jordan, Hoffman, Bloom, & Rand, 2016).

One approach to explaining why moral intuitions often align withdeontology comes from mutualistic partner choice models of theevolution of morality. These models posit a cooperation market suchthat agents who can be relied upon to act in a mutually beneficial wayare more likely to be chosen as cooperation partners, thus increasingtheir own fitness

intriguingly

nd recent theoretical work has demon-strated that “cooperating without looking”—that is, without consid-ering the costs and benefits of cooperation—is a subgame perfectequilibrium (Hoffman, Yoeli, & Nowak, 2015). Therefore, expressingcharacteristically deontological judgments could constitute a behaviorthat enhances individual fitness in a cooperation market because thesejudgments are seen as reliable indicators of a specific valued behav-ior—cooperation

Across 5 studies, we show that people who make characteristically deontological judgments arepreferred as social partners, perceived as more moral and trustworthy, and are trusted more in economicgames.

Table 3also suggests that conditional norm enforcement is more pronounced among the populationwith intermediate and high levels of education. This finding is consistent with the observationthat conditional cooperation is particularly robust in lab experiments with student subjectpools (see G ̈achter, 2007). The data further show that females tend to be more inclined tosanction, in particular deviations from the strong norms. In contrast, employed respondentsare less engaged in sanctioning. All other socioeconomic characteristics do not show a clear

Ina national survey conducted in Austria, respondents were confronted with eight different‘incorrect behaviors’, including tax evasion, drunk driving, fare dodging or skiving off work.Respondents were then asked how they would react if an acquaintance followed such behavior.The response categories cover positive reactions – like approval (Rege and Telle, 2004) – aswell as negative reactions like cooling down the contact or expressing disapprova

A dissertation or final-year project allows you to explore your aptitude for, and interest in doing economic research

James, Gareth; Witten, Daniela; Hastie, Trevor; Tibshirani, Robert. (2013) An introduction to statistical learning: with applications in R, New York: Springer. vol. Springer texts in statistics

- construct factorial experiments in blocks;

Overleaf /LaTex 

f you can avoid assigning subjects to treatments by cluster, you should.

fit_simple <- lm(Y_simple ~ Z_simple, data=hec)

This complication is typically addressed in one of two ways: “controlling for blocks” in a regression context, or inverse probability weights (IPW), in which units are weighted by the inverse of the probability that the unit is in the condition that it is in.

The gains from a blocked design can often be realized through covariate adjustment alone.

Of course, such heterogeneity could be explored if complete random assignment had been used, but blocking on a covariate defends a researcher (somewhat) against claims of data dredging.

In this simulation complete random assignment led to a -0.59% decrease in sampling variability. This decrease was obtained with a small design tweak that costs the researcher essentially nothing.

with(hec, mean(Y1 - Y0))

# Reveal observed potential outcomes

when deploying a survey experiment on a platform like Qualtrics, simple random assignment is the only possibility due to the inflexibility of the built-in random assignment tools.

Since you need to know N beforehand in order to use simple_ra(), it may seem like a useless function.

depending on the random assignment, a different number of subjects might be assigned to each group.

Y0 <- rnorm(n = N,mean = (2*as.numeric(Hair) + -4*as.numeric(Eye) + -6*as.numeric(Sex)), sd = 5)

hec <- within(hec,{

Solution! Re: Export To Excel Mark as New Bookmark Subscribe Mute Subscribe to RSS Feed Permalink Print Email to a Friend Report Inappropriate Content slipstream42 Regular ‎2017-07-31 04:22 PM another csv export link it is quite nicehttps://rawgit.com/watsonbox/exportify/master/exportify.htmlcode on github  View solution in original post 31 Likes

As you can see, having one fewer child still comes out looking like a solid way to reduce carbon emissions — but it’s absolutely nowhere near as effective as it first seemed. It no longer dwarfs the other options. On this model, instead of having one fewer kid, you can skip a couple of transatlantic flights and you’ll save the same amount of carbon. That seems like a way more manageable sacrifice if you’re a young person who longs to be a parent.

commas <- function(...) stringr::str_c(..., collapse = ", ")

it’s the same as the input!

Compute the mean of every column in mtcars.

output <- vector("double", ncol(mtcars))  # 1. output
for (i in seq_along(mtcars)) {            # 2. sequence
  output[[i]] <- mean(mtcars[[i]])      # 3. body
}

The rational expectation and thelearning-from-price literatures argue that equilibrium prices are accurate becausethey reveal and aggregate the information of all market participants. The MarketSelection Hypothesis,MSH, proposes instead that prices become accurate becausethey eventually reflect only the beliefs of the most accurate agent. The Wisdomof the Crowd argument,WOC, however suggests that market prices are accuratebecause individual, idiosyncratic errors are averaged out by the price formationmechanism

external fundraising page

Fundraising Dashboard / Participant Center Visited When a person visits their fundraising dashboard or participant center

Fundraising Page Created / Registration Complete Upon completion of the last step of the registration flow that creates a fundraising page

Contributing to the textbook Use Hypothes.is, an amazing tool for annotating the web. Go to Hypothes.is, and “get-started”

    includes:
      in_header: [header_include.html]

<script async defer src="https://hypothes.is/embed.js"></script>

head(as.data.frame(nasa))#> lat long month year cloudhigh cloudlow cloudmid ozone pressure #> 1 36.20000 -113.8 1 1995 26.0 7.5 34.5 304 835 #> 2 33.70435 -113.8 1 1995 20.0 11.5 32.5 304 940 #> 3 31.20870 -113.8 1 1995 16.0 16.5 26.0 298 960 #> 4 28.71304 -113.8 1 1995 13.0 20.5 14.5 276 990 #> 5 26.21739 -113.8 1 1995 7.5 26.0 10.5 274 1000 #> 6 23.72174 -113.8 1 1995 8.0 30.0 9.5 264 1000 #> surftemp temperature #> 1 272.7 272.1 #> 2 279.5 282.2 #> 3 284.7 285.2 #> 4 289.3 290.7 #> 5 292.2 292.7 #> 6 294.1 293.6

Now this can be simplified using the new {{}} syntax: summarise_groups <- function(dataframe, grouping_var, column_name){ dataframe %>% group_by({{grouping_var}}) %>% summarise({{column_name}} := mean({{column_name}}, na.rm = TRUE)) } Much easier and cleaner! You still have to use the := operator instead of = for the column name however. Also, from my understanding, if you want to modify the column names, for instance in this case return "mean_height" instead of height you have to keep using the enquo()–!! syntax.

(1) “How likely do you think it is that this hypothesis will be replicated (on a scale from 0% to 100%)?” (2) “How large do you think the standardized effect size (in terms of Cohen’s d) from the replication will be, relative to that in the original paper (on a scale from −50% to 200%)?”, and (3) “How well do you know this topic? (Not at all; Slightly; Moderately; Very well; Extremely well.)”

0.506 (0.532)

For the 12 studies with an original p < 0.005, 10 (83%) replicated. For the 12 studies with an original p > 0.005, only 1 (8%) replicated. Further work is needed to test if prediction markets outperform predictions based only on the initial p-value, to test if the market also aggregates other information important for reproducibility.

At least one of my un-named research co-authors will heartily agree with this statement.↩︎

ps f

List previous command history: history

It’s worth noting that first line of the script starts with #!. It is a special directive which Unix treats differently.

Happy Git and GitHub for the useR

8 Writing, argumentation, presentation, and (Economic) logic: Being clear and making sense

Prediction in Policy

Suppose the algorithm chooses a tree that splits on education but not on age. Conditional on this tree, the estimated coefficients are consistent. But that does not imply that treatment effects do not also vary by age, as education may well covary with age; on other draws of the data, in fact, the same procedure could have chosen a tree that split on age instead

hese heterogenous treatment effects can be used to assign treatments; Misra and Dubé (2016) illustrate this on the problem of price targeting, applying Bayesian regularized methods to a large-scale experiment where prices were randomly assigned

Chernozhukov, Chetverikov, Demirer, Duflo, Hansen, and Newey (2016) take care of high-dimensional controls in treatment effect estimation by solving two simultaneous prediction problems, one in the outcome and one in the treatment equation.

In particular, a set of papers has already introduced regu-larization into the first stage in a high-dimensional setting, including the LASSO (Belloni, Chen, Chernozhukov, and Hansen 2012) and ridge regression (Carrasco 2012; Hansen and Kozbur 2014

These same techniques applied here result in split-sample instrumental variables (Angrist and Krueger 1995) and “jackknife” instrumental variables

Understood this way, the finite-sample biases in instrumental variables are a consequence of overfitting.

Even when we are interested in a parameter β ˆ, the tool we use to recover that parameter may contain (often implicitly) a prediction component. Take the case of linear instrumental variables understood as a two-stage procedure: first regress x = γ′z + δ on the instrument z, then regress y = β′x + ε on the fitted values x ˆ. The first stage is typically handled as an estimation step. But this is effectively a prediction task: only the predictions x ˆ enter the second stage; the coefficients in the first stage are merely a means to these fitted values.

Prediction in the Service of Estimation

New Data

Zhao and Yu (2006) who establish asymptotic model-selection consistency for the LASSO. Besides assuming that the true model is “sparse”—only a few variables are relevant—they also require the “irrepresentable condition” between observables: loosely put, none of the irrelevant covariates can be even moderately related to the set of relevant ones.

First, it encourages the choice of less complex, but wrong models. Even if the best model uses interactions of number of bathrooms with number of rooms, regularization may lead to a choice of a simpler (but worse) model that uses only number of fireplaces. Second, it can bring with it a cousin of omitted variable bias, where we are typically concerned with correlations between observed variables and unobserved ones. Here, when regular-ization excludes some variables, even a correlation between observed variables and other observed (but excluded) ones can create bias in the estimated coefficients.

97the variables are correlated with each other (say the number of rooms of a house and its square-footage), then such variables are substitutes in predicting house prices. Similar predictions can be produced using very different variables. Which variables are actually chosen depends on the specific finite sample.

Through its regularizer, LASSO produces a sparse prediction function, so that many coefficients are zero and are “not used”—in this example, we find that more than half the variables are unused in each run

One obvious problem that arises in making such inferences is the lack of stan-dard errors on the coefficients. Even when machine-learning predictors produce familiar output like linear functions, forming these standard errors can be more complicated than seems at first glance as they would have to account for the model selection itself. In fact, Leeb and Pötscher (2006, 2008) develop conditions under which it is impossible to obtain (uniformly) consistent estimates of the distribution of model parameters after data-driven selection.

First, econometrics can guide design choices, such as the number of folds or the function class.

These choices about how to represent the features will interact with the regularizer and function class: A linear model can reproduce the log base area per room from log base area and log room number easily, while a regression tree would require many splits to do so.

Ta b l e 2Some Machine Learning Algorithms

Picking the prediction func-tion then involves two steps: The first step is, conditional on a level of complexity, to pick the best in-sample loss-minimizing function.8 The second step is to estimate the optimal level of complexity using empirical tuning (as we saw in cross-validating the depth of the tree).

egularization combines with the observability of predic-tion quality to allow us to fit flexible functional forms and still find generalizable structure.

This procedure works because prediction quality is observable: both predic-tions y ˆ and outcomes y are observed. Contrast this with parameter estimation, where typically we must rely on assumptions about the data-generating process to ensure consistency.

In empirical tuning, we create an out-of-sample experiment inside the original sample.

Performance of Different Algorithms in Predicting House Values

We consider 10,000 randomly selected owner-occupied units from the 2011 metropolitan sample of the American Housing Survey. In addition to the values of each unit, we also include 150 variables that contain information about the unit and its location, such as the number of rooms, the base area, and the census region within the United States. To compare different prediction tech-niques, we evaluate how well each approach predicts (log) unit value on a separate hold-out set of 41,808 units from the same sample. All details on the sample and our empirical exercise can be found in an online appendix available with this paper athttp://e-jep.org

Making sense of complex data such as images and text often involves a prediction pre-processing step.

The fundamental insight behind these breakthroughs is as much statis-tical as computational. Machine intelligence became possible once researchers stopped approaching intelligence tasks procedurally and began tackling them empirically.

Why not also use it to learn something about the “underlying model”: specifically, why not use it to make infer-ences about the underlying data-generating process?

Economic theory and content expertise play a crucial role in guiding where the algorithm looks for structure first. This is the sense in which “simply throw it all in” is an unreasonable way to understand or run these machine learning algo-rithms.

available finite-sample guidance on its implementation—such as heuristics for the number of folds (usually five to ten) or the “one standard-error rule” for tuning the LASSO (Hastie, Tibshirani, and Friedman 2009)—has a more ad-hoc flavor.

Should out-of-sample performance be estimated using some known correction for overfitting (such as an adjusted R2 when it is available) or using cross-validation?

Kernel regressionKernel bandwidth

final category is in direct policy applications. Deciding which teacher to hire implicitly involves a prediction task (what added value will a given teacher have?), one that is intimately tied to the causal question of the value of an additional teacher.

In another category of applications, the key object of interest is actually a parameter β, but the inference procedures (often implicitly) contain a prediction task. For example, the first stage of a linear instrumental variables regres-sion is effectively prediction. The same is true when estimating heterogeneous treatment effects, testing for effects on multiple outcomes in experiments, and flexibly controlling for observed confounders.

Machine Learning: An Applied Econometric Approach

David Chalmers: I think I may have introduced this actually years ago. I call it “The law of minimization of mystery”. I was making fun of some people who wanted to tie consciousness and quantum mechanics. But I do think there are interesting potential links between the two. I mean. The problem in quantum mechanics is not just that it’s mysterious.It’s a very specific problem. How do the standard dynamics of quantum mechanics which has these two processes: Schrodinger evolution and wave function collapse. Mostly the wave function evolves this way, except on certain times, when you make a measurement, the wave function changes in this special way, and that’s totally standard quantum mechanics.