This course will cover the steps used in weighting sample surveys, including methods for adjusting for nonresponse and using data external to the survey for calibration. Among the techniques discussed are adjustments using estimated response propensities, poststratification, raking, and general regression estimation. Alternative techniques for imputing values for missing items will be discussed. For both weighting and imputation, the capabilities of different statistical software packages will be covered, including R®, Stata®, and SAS®.
Quantities to Estimate
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Dealing With Missing Data
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University of Maryland, College Park
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课程 5（共 7 门，Specialization Survey Data Collection and Analytics ）
从本节课中
General Steps in Weighting
Weights are used to expand a sample to a population. To accomplish this, the weights may correct for coverage errors in the sampling frame, adjust for nonresponse, and reduce variances of estimators by incorporating covariates. The series of steps needed to do this are covered in Module 1.
与讲师见面
Richard Valliant, Ph.D.Research Professor
Joint Program in Survey Methodology
In this second part of module 1 of course 5,
we'll look at quantities that we can estimate using survey weights.
Some of the most important things, or basic things, are totals.
So we might want to estimate the total
number of persons on a public assistance program, the total number of
days that people have spent without jobs in some economy.
The number of visits to a doctor in the last few year.
All those are things that may be of interest in different kinds of surveys.
One thing that makes this somewhat easy
to think about is that we can write a population total in the following way.
We've got the sample units that we observed.
We don't have to estimate anything for them, we observed the data for them.
So we sum those values up.
This notation here, i and
element of the s means I sum over the units high that are in the set s.
So an s stands for the sample units.
So, I sum those up.
And then, the second part of the population total
are the things that I did not see, we had the scene in the sample.
The unseen part in the non-sample.
So, little r stands for the remainder of the non-sample units.
And our job in estimating a total is pretty straightforward.
We need to predict this sum for the non-sample units, and
there are various ways of doing that.
Usually, an estimated total has got this form right here.
We sum up the units in the sample, we take the weight that we assign them,
times their data value.
And assuming again that these weights are scaled to estimate population
totals then we'll get a legitimate estimate of the finite population total.
We can estimate other things.
Means are interesting quantities.
We might want to estimate the average income,
the average number of years of schooling per person,
students' average test score on some standardized test.
The standard way of doing that is to take an estimate of the total.
That's this first piece, the sum over the sample of the weights times the data.
And then divided by the sum of the weights.
So you can see that these scales thing is it about the right way.
But one thing to note here,
the weights are normally calculated, the sum of the weights
is going to be an estimate of the number of units in a population.
Sometimes it's exactly equal to the number of units in the population,
it depends on how we calculate the weights and what type of samples is drawn.
In general though it's an estimate.
If we sum over a subset, a subgroup, say just over the men or the women.
That's going to be an estimate of the number of units in that sub-group.
So it's a useful characteristic which follow those examples in the way
we calculate weight there, the sum of the weight Is an estimate of a count of U,
that's for whatever group that we do the summing of.
Now we can estimate the other things, some important things that
surveys usually put out are proportions or percentages.
For example a percentage of persons who plan to vote for a candidate or
the unemployment rate, those are proportions.
We can estimate quantiles like medians, in the 1st and 3rd quartiles.
And for example median household income, median age at first marriage.
We could estimate the 95.5th percentile of blood level in children, age 1 to 5,
which happens to be a percentile that public health people are interested in.
So here's the algorithm for estimating quantile.
The first thing you do, is sort the file from low to
high along the y value that you're talking about.
So it could be blood lead content for example.
And then you cumulate the weights until the desired percent of total weight
is reached.
So 50% for the median for example.
So notice when I cumulate weights, that's summing over a subgroup.
If I sum to the halfway point, that's an estimate of the number of
people whose y value is 50%,
is equal to that y value or less.
And if I sum to the halfway point, that's the 50th percentile or the median.
So I record the value of y for that unit that I've summed up to and
that's my sample estimate of the median or whatever quantile that I'm interested in.
And we can also estimate things like ratios.
We could estimate say that the ratio women's average income to men's average
income, which might be an interesting quantity.
We can estimate odds rations in a 2x2 table.
For example the ratio of the odds of having diabetes for
African Americans to the odds for all others.
And we can also estimate regression model parameters with weighted estimates.
Now the important thing that occurs in these situations
is that many of the things that I've talked about like ratios, or
odds ratios, or proportions,
means are all functions of estimated totals.
So if we understand how to estimate totals,
we're a long way along toward the problem of
understanding how to estimate many other things in finite populations.
Another thing that is critical in most
surveys is to make estimates for subgroups.
So for example, if I wanted the proportion of males age 18 to 34
who watched the live sports event on television, that's a subgroup.
If I did a cross tab of gender by a number of age groups.
In each cell in that cross tab, if I estimate this proportion of people who
watch the sporting event, those are subgroup estimates or domain estimates.
So it's common.
Every time you do a cross table in, from survey data,
you're making domain or subgroup estimates.
Now one thing that needs to be accounted for in many cases is the effect
on standard errors of the fact that we may not control sample size,
in every cell in the table that we do.
So you can account for that randomness in a specific way.
Sometimes the cells are strata where we control the sample size.
And in that case we can treat it as fixed.
But otherwise, what showed up in our sample is random, and
typically we try to account for that.
So in the next section we'll talk about some more of the goals of estimation.
