‘Representativeness heuristic’, base rates, and Bayes

April 23, 2012 in General | Permalink

From the Introduction of their edited volume:
Tversky and Kahneman used the following experiment for testing ‘representativeness heuristic’ –

Subjects are shown a brief personality description of several individuals, sampled at random from 100 professionals – engineers and lawyers.
Subjects are asked to assess whether description is of an engineer or a lawyer.
In one condition, subjects are told group = 70 engineers/30 lawyers. Another the reverse = 70 lawyers/30 engineers.

Results -
Both conditions produced same mean probability judgments.

Discussion -
Tversky and Kahneman call this result a ‘sharp violation’ of Bayes Rule.

Counter Point -
I am not sure the experiment shows any such thing. Mathematical formulation of the objection is simple and boring so an example. Imagine, there are red and black balls in an urn. Subjects are asked if the ball is black or red under two alternate descriptions of the urn composition. When people are completely sure of the color, the urn composition obviously should have no effect. Just because there is one black ball in the urn (out of say a 100), it doesn’t mean that the person will start thinking that the black ball in her hand is actually red. So on and so forth. One wants to apply Bayes by accounting for uncertainty. People are typically more certain (lots of evidence it seems – even in their edited volume) so that automatically discounts urn composition. People may not be violating Bayes Rule. They may just be feeding the formula incorrect data.

State of the union

March 22, 2012 in Politics | Permalink

Over the past forty years, Proportion of Respondents Reporting At least one union member in the household has declined precipitously. (Source American National Election Studies) .

Interviewer Assesments of Respondent’s Level of Political Information

March 15, 2012 in Politics | Permalink

In the National Election Studies (NES), interviewers have been asked to rate respondent’s level of political information – “Respondent’s general level of information about politics and public affairs seemed – Very high, Fairly high, Average, Fairly low, Very low.” John Zaller, among others, have argued that these ratings measure political knowledge reasonably well. However there is some evidence that challenges the claim. For instance, there is considerable unexplained inter and intra-interviewer heterogeneity in ratings – people with similar levels of knowledge (as measured via closed-ended items) are rated very differently (Levendusky and Jackman 2003 (pdf)). It also appears that mean interviewer ratings have been rising over the years, compared to the relatively flat trend observed in more traditional measures (see Delli Carpini, and Keeter 1996 and Gilens, Vavreck, and Cohen 2004, etc).

Part of the increase is explained by higher ratings of respondents with less than a college degree; ratings of respondents with BS or more have remained somewhat more flat. As a result, difference in ratings of people with a Bachelor’s Degree or more and those with less than a college degree is decreasing over time. Correlation between interviewer ratings and other criteria like political interest are also trending downward (though decline is less sharp). This conflicts with evidence for increasing ‘knowledge gap’ (Prior 2005).

The other notable trend is the sharp negative correlation (over .85) between intercept and slope of within-year regressions of interviewer ratings and political interest, education, etc. This sharp negative correlation hints at possible ceiling effects. And indeed there is some evidence for that.

Interviewer Measure – The measure is sometimes from the pre-election wave only, other times in the post-election wave only, and still other times in both waves. Where both pre and post measures were available, they were averaged. The correlation between pre-election and post-election rating was .69. The average post-election ratings are lower than pre-election ratings.

Comparing datasets, reporting only non-duplicated rows

February 27, 2012 in R | Permalink

The following is in response to question on the R-Help list.

Consider two datasets –

reported <-
structure(list(Product = structure(c(1L, 1L, 1L, 1L, 2L, 2L,
3L, 4L, 5L, 5L), .Label = c(“Cocoa”, “Coffee C”, “GC”, “Sugar No 11″,
“ZS”), class = “factor”), Price = c(2331, 2356, 2440, 2450, 204.55,
205.45, 17792, 24.81, 1273.5, 1276.25), Nbr.Lots = c(-61L, -61L,
5L, 1L, 40L, 40L, -1L, -1L, -1L, 1L)), .Names = c(“Product”,
“Price”, “Nbr.Lots”), row.names = c(1L, 2L, 3L, 4L, 6L, 7L, 5L,
10L, 8L, 9L), class = “data.frame”)

exportfile <-
structure(list(Product = c(“Cocoa”, “Cocoa”, “Cocoa”, “Coffee C”,
“Coffee C”, “GC”, “Sugar No 11″, “ZS”, “ZS”), Price = c(2331,
2356, 2440, 204.55, 205.45, 17792, 24.81, 1273.5, 1276.25), Nbr.Lots = c(-61,
-61, 6, 40, 40, -1, -1, -1, 1)), .Names = c(“Product”, “Price”,
“Nbr.Lots”), row.names = c(NA, 9L), class = “data.frame”)

Two possible solutions -
A.
m <- rbind(reported, exportfile)
m1 <- m[duplicated(m),]
res <- m[is.na(match(m$key, m1$key)),]

B.

exportfile$key <- do.call(paste, exportfile)
reported$key <- do.call(paste, reported)
a <- reported[is.na(match(reported$key, exportfile$key)),]
b <- exportfile[is.na(match(exportfile$key, reported$key)),]
res <- rbind(a, b)

Correcting for Differential Measurement Error in Experiments

February 14, 2012 in General | Permalink

Differential measurement error across control and treatment groups or (pre and post-treatment measurement waves) can vitiate estimates of treatment effect. One prominent reason for differential error in survey context is differential motivation. For instance, if participants are less motivated to respond accurately on the pre-treatment survey than on the post-treatment survey (or respondents satisfice more on the pre-treatment survey that post-treatment survey), the pre-post difference score will be a biased estimator of the treatment effect. Weiksner (2008) provides an empirical example of the broad problem that he identifies – participants ‘acquiesce’ more during the pre-treatment (treatment is the Deliberative Poll) survey than the post-treatment survey, compromising inferences about how many much attitude change happens over the course of the treatment. To correct for it, one may want to replace agree/disagree responses with construct specific questions (Weiksner, 2008). A perhaps better solution would be to incentivize all (or a random subset of) responses to the pre-treatment survey. Possible incentives include – monetary rewards, adding a preface to the screens telling people how important accurate responses are to research, etc. This is the same strategy that I advocate for dealing with satisficing more generally (see here) – which translates to minimizing errors, than the dominant though somewhat more suboptimal strategy of “balancing errors” by randomizing the response order.

Against Proxy Variables

December 23, 2011 in Research | Permalink

Lacking direct measures of the theoretical variable of interest, some scholars rely on ‘proxy variables’. For instance, some have used years of education as a proxy for cognitive ability. However, using ‘proxy variables’ can be problematic for the following reasons – (1) proxy variables may not track the theoretical variable of interest very well, (2) they may track other confounding variables, outside the theoretical variable of interest. For instance, in the case of years of education as a proxy for cognitive ability, the concerns manifest themselves as follows –

1) Cognitive ability causes, and is a consequence of, what courses you take, and what school you go to, in addition to of course, years of education. GSS for instance contains more granular measures of education – for instance did the respondent take science course in college. And nearly always the variable proves significant when predicting knowledge, etc. This all is somewhat surmountable as it can be seen as measurement error.

2) More problematically, years of education may tally other confounding variables –diligence, education of parents, economic strata, etc. And then education endows people with more than cognitive ability; it also causes potentially confounding variables such as civic engagement, knowledge, etc.

Conservatively we can only attribute the effect of the variable to the variable itself. That is – we only have variables we enter. If one does rely on ‘proxy variables’ then one may want to address the two points mentioned above.

Education and Economic Inequality

December 7, 2011 in General | Permalink

Across UK and US, a large majority of politicians seem to believe that increasing levels of education will reduce economic inequality. However it isn’t clear if the policy is empirically supported. Here are some potential ways increasing levels of education can impact economic inequality –

  1. As Grusky argues, the current high wage earners whose high wages depend on education and lack of competition from similarly educated men and women (High Education Low Competition or HELCO) from similarly highly educated will start earning a lower wage because of increased competition (thereby reducing inequality). This is assuming that HELCO won’t respond by trying to burnish their education credentials, etc. This is also assuming that HELCO exists as a large class. What likely exists, instead of HELCO, success attributable to networks, etc. That kind of advantage cannot be blunted by increasing education among those ‘not in the network’.
  2. Another possibility is that education increases the number of high paying jobs available in the economy and it raises the boats of non-HELCO more than HELCO. There is some evidence for that, though mostly anecdotal.
  3. Another plausible scenario is that additional education produces only a modest effect with non-HELCO still mostly doing low paying jobs. This may due to only a modest increase in overall availability of ‘good jobs’. This outcome is in fact likely if data are any indication. Already easy access to education has meant that many a janitor, and store clerks walk around with college degrees (see Why Did 17 Million Students Go to College?, and The Underemployed College Graduate).

Without an increase in ‘good jobs’, the result of increase in education is an increased heterogeneity in who succeeds (random draw at the extreme) but no change in proportion of those successful. Or, increasing equality of opportunity (a commendable goal) but not reduction in economic inequality (though in a multi-generation game, it may even out). Increasing access to education also has the positive externality of producing a more educated society, another worthy goal.

How plentiful the ‘good jobs’ are depends partly on how the economic activity is constructed. For instance, there may have once have been a case for only hiring one ‘super-talented person’ (say ‘superstar’) for a top shelf job (say CEO). Now we have systems that can harness the wisdom of many. It is also plausible that that wisdom is greater than that of the superstar. It reasons then that the superstar be replaced; economic activity will be more efficient. Or else let other smart people who can contribute equally (if educated) be recompensed alternately for doing work that is ‘beneath them’.

R – Recoding variables reliably and systematically

November 12, 2011 in R | Permalink

Survey datasets typically require a fair bit of repetitive recoding of variables. Reducing errors in recoding can be done by writing functions carefully (see some tips here) and automating and systematizing naming, and application of the recode function (which can be custom) –

fromlist <- c(“var1″, “var2″, “var3″, “var4″, “var5″)
tolist <- paste(c(“var1″, “var2″, “var3″, “var4″, “var5″), “recoded”, sep=”")
data[,tolist] <- sapply(data[,fromlist], function(x) car::recode(x , “recode.directions”))

Simple functions can also be directly applied to each column of a data.frame. For instance,
data[,tolist] <- !is.na(data[,fromlist])
data[,tolist] <- abs(data[,fromlist] – .5)

Measuring Impact of Media

November 10, 2011 in Research | Permalink

Measuring the impact of media accurately has proven a challenge. Findings of minimal effects abound when intuition tells us that an activity that an average American engages in over forty hours a week is likely to have a larger impact. These insignificant findings have been typically attributed to frailty of survey self-reports of media exposure, though debilitating error in dependent variables has also been noted as a culprit. Others have noted weaknesses in research design, inadequate awareness of analytic techniques that allow one to compensate for error in measures, etc. as stumbling blocks.

Here are a few of the methods that have been used to overcome some of the problems in media research, along with some modest new proposals of my own –

  • Measurement
    Since measures are error prone, one strategy has been to combine multiple measures. Multiple measures of a single latent concept can be combined using latent variable models, factor analysis, or even simple averaging. Precaution must be taken to check that errors across measures aren’t heavily correlated, for under such conditions improvements from combining multiple measures are likely to be weak or non-existent. In fact deleterious effects are possible.

    Another point of worry is that measurement error can be correlated with irrelevant respondent characteristics. For instance, women guess less than men on knowledge questions. Hence responses to knowledge questions are a function of ability and propensity to guess when one doesn’t know (tallied here by gender). By conditioning on gender, we can recover better estimates of ‘ability’. Another application would be in handling satisficing.

  • Measurement of exposure
    Rather than use self-assessments of exposure, which have been shown to be correlated to confounding variables, one may want to track incidental consequences of exposure as a measure for exposure. For example, knowledge of words of a campaign jingle, attributes of a character in a campaign commercial, source (~channel) on which the campaign was shown, program, etc. These measures factor in attention, in addition to exposure, which is useful. Unobtrusive monitoring of consumption is of course likely to be even more effective.

  • Measurement of Impact
    1. Increased exposure to positive images ought to change procedural memory and implicit associations. One can use IAT or AMP to assess the effect.
    2. Tracking Twitter and Facebook feeds for relevant information. These measures can be calibrated to opinion poll data to get a sense of what they mean.
  • Data Collection
    1. Data collection efforts need to reflect half-life of the effect. Recent research indicates that some of the impact of the media may be short-lived. Short-term effects may be increasingly consequential as people increasingly have the ability to act on their impulses – be it buying something, or donating to a campaign, or finding more information about the product. Behavioral measures (e.g. website hits) corresponding to ads may thus be one way to track impact.
    2. Future ‘panels’ may contain solely passive monitoring of media use (both input and output) and consumption behavior.
  • Estimating recipient characteristics via secondary data
    1. Geocoded IP addresses can be used to harvest secondary demographic data (race, income, etc.) from census
    2. Para-data like what browser and operating system the customer uses etc. are reasonable indicators of tech. savvy. And these data are readily harvested.
    3. Datasets can be merged via ‘matching’ or by exploiting correlation across items and by calibrating.

Working with modestly large datasets in R

November 2, 2011 in R | Permalink

Even modestly large (< 1 GB) datasets can quickly overwhelm modern personal computers. Working with such datasets in R can be still more frustrating because of how R uses memory. Here are a few tips on how to work with modestly large datasets in R.

Setting Memory Limits
On Windows, right click R and in the Target field set maximum vector size and memory size as follows –
“path\to\Rgui.exe” –max-vsize=4800M (Deprecated as of 2.14).

Alternately, use utils::memory.limit(size=4800) in .Rprofile.

Type in mem.limits() to check maximum vector size
Learn more

Reading in CSVs
Either specify column classes manually or get the data type for each column by reading in the first few rows – enough so that data type can be inferred correctly – and using the class that R is using.

# Read the first 10 rows to get the classes
ads5 <- read.csv("data.csv", header=T, nrows=10)
classes <- sapply(ads5, class)

Specifying number of rows in the dataset (even a modestly greater number than what is there) can be useful.
read.csv("data.csv", header=T, nrows=N, colClasses=classes)

Improvements in performance are not always stupendous but given the low cost of implementation, likely worthwhile.

Selective Reading
You can selectively read columns by specifying colClasses=NULL for the columns you don’t want read.
Alternately, you can rely on cut. For instance,
data <- read.table(pipe("cut -f 2,5 -d, data.csv"))

Opening Connections
Trying to directly read csv can end in disaster. Open a connection first to reduce memory demands.
abc <- file("data.csv")
bbc <- read.csv(abc)

Using SQLDF
library(sqldf)
f <- file("data.csv")
Df <- sqldf("select * from f", dbname=tempfile(), file.format=list(header=T, row.names=F))
Problems include inability to deal with fields which have commas etc.

Using Filehash

Filehash package stores files on the hard drive. You can access the data using either with() if dealing with env variable, or directly via dbLoad() that mimics functionality of attach. Downside: it is tremendously slow.

library(filehash)
dumpDF(read.csv(“data.csv”, header=T, nrows=N, colClasses=classes), dbName=”db01″)
ads <- db2env(db ="db01")

Selecting Columns
Use subset(data, select=columnList) rather than data[, columnList].

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