[R] Linear regression with a rounded response variable

[peter salzman]

here is one thought:

if you plug in your numbers into any kind of regression you will get
prediction that are real numbers and not necessarily integers, it may be
that you predictions are good enough with this approximate value of Y. you
could test this by randomly shuffling your data by +- 0.5 and compare the
results with the original result.

let me add another idea:

if data is not fully observed this falls under the umbrella of censored
data, in this case you have interval censoring. if you see 5 then the
observations is in interval [4.5, 5.5]
i'm not familiar with the field but i'd search for 'regression with
interval censoring'


peter


On Wed, Oct 21, 2015 at 10:53 AM, Ravi Varadhan <ravi.varadhan at jhu.edu>
wrote:

> Hi,
> I am dealing with a regression problem where the response variable, time
> (second) to walk 15 ft, is rounded to the nearest integer.  I do not care
> for the regression coefficients per se, but my main interest is in getting
> the prediction equation for walking speed, given the predictors (age,
> height, sex, etc.), where the predictions will be real numbers, and not
> integers.  The hope is that these predictions should provide unbiased
> estimates of the "unrounded" walking speed. These sounds like a measurement
> error problem, where the measurement error is due to rounding and hence
> would be uniformly distributed (-0.5, 0.5).
>
> Are there any canonical approaches for handling this type of a problem?
> What is wrong with just doing the standard linear regression?
>
> I googled and saw that this question was asked by someone else in a
> stackexchange post, but it was unanswered.  Any suggestions?
>
> Thank you,
> Ravi
>
> Ravi Varadhan, Ph.D. (Biostatistics), Ph.D. (Environmental Engg)
> Associate Professor,  Department of Oncology
> Division of Biostatistics & Bionformatics
> Sidney Kimmel Comprehensive Cancer Center
> Johns Hopkins University
> 550 N. Broadway, Suite 1111-E
> Baltimore, MD 21205
> 410-502-2619
>
>
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>
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-- 
Peter Salzman, PhD
Department of Biostatistics and Computational Biology
University of Rochester

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