Date post: | 17-Dec-2015 |
Category: |
Documents |
Upload: | darren-gaines |
View: | 213 times |
Download: | 0 times |
Exploratory Analysis of Survey Data
Lisa Cannon
Luke Peterson
Presentation Outline
Density Estimation Nonparametric kernel density estimates Properties of kernel density estimators Other methods
Graphical Displays NHANES data
Three features that distinguish survey data:
1. Individuals in the sample represent differing numbers of individuals in the population - sampling weights used to estimate this.
2. Some data imputed due to item nonresponse.
3. Sample sizes can be quite large.
The Need for Nonparametric Methods We often study point estimation that assumes iid
random variables. Stratification may result in violation of identically
distributed random variables Clustering may result in violation of independence Methods we discuss use asymptotic properties that
allow nonparametric methods for estimating shape of a distribution
Kernel Density Estimates
Bellhouse and Stafford (1999) looked at kernel density estimation for The whole data set Binned data (groups the data after it is smoothed) Smoothing binned data (smooths the data after it
is grouped) Asymptotic integrated MSE for model-based
and design-based derived.
Why Binning?
To simplify estimation of large samples The shape of the data can be distorted by
binning Smoothing helps to recover lost structure
Design-Based and Model-Based
Different ways to handle the asymptotics Model-based: N finite population units are a
sample of identically distributed units from infinite super-population
Design Based: A nested sequence of N finite populations, where the distribution function of these populations converges as
Weights do not affect bias, but the estimation of variance is inflated by the value for the design effect
N
Buskirk and Lohr (2005)
Also addressed kernel density estimation Considers use of whole data (no binning) Also considered a combination of design-
based and model-based approaches Explore conditions for consistency and
asymptotic normality Defined confidence bands for the density
Applications
Ontario Health Survey US National Crime Victimization Survey
(NCVS) US National Health and Nutrition
Examination Survey (NHANES)
Other Methods
Bellhouse, Stafford (2001)– Polynomial regression methods
Bellhouse, Chipman, Stafford (2004)– Additive models for survey data via penalized least squares method
Korn et al. (1997) – Smoothing the empirical cumulative distribution function
Graubard, Korn (2002)– Variance estimation Many others
Plotting Survey Data
Common difficulties with plotting survey data:
Dealing with sampling weights Plotting a large number of observations can be
difficult to interpret See Korn and Graubard (1998).
National Health and Nutrition Survey (NHANES)
Has been conducted on a periodic basis since 1971.
Completes about 7,000 individual interviews annually.
Analyzes risk factor for selected diseases and conditions.
Sample implemented is a stratified multistage design.
Data available at http://www.cdc.gov/nhanes
Glycohemoglobin Level (Ghb)
A blood test that measures the amount of glucose bound to hemoglobin.
Normally, about 4% to 6%. People with diabetes have more
glycohemoglobin than normal. The test indicates how well diabetes has
been controlled in the 2 to 3 months before the test.
Source: http://my.webmd.com
Histograms
Histograms provide a nice summary of the distribution of large data sets.
Suppose that we would like to assess the distribution of glycohemoglobin levels.
Sampling weights must be considered before plotting a histogram.
SAS Code: Account for Weightsproc univariate data=explore.glyco noprint;
var glyco;
freq weight;
histogram / nrows=2 cfill=red midpoints=3 to 15 by 0.5 cgrid=grayDD;
run; The variable weight indicates the number of
population units the sample unit represents.
Histograms – Effect of Sampling Weights
Boxplots
Boxplots indicate location of important summary statistics along with distribution.
See Figures 7.8 and 7.10 in Lohr. The boxplot procedure in SAS will not accept
any arguments to account for weights. The survey library in R will.
Graphs for Regression – Bubble Plots Scatterplots are inadequate for survey data
as they fail to account for sampling weights. Bubble plots incorporate the weights by
making the area of each circle proportional to the number of population observations at those coordinates (See Lohr, Chapter 11).
The ordinary least squares regression line is then replaced by a weighted least squares line.
See Figure 11.5 in Lohr
Bubble Plot for NHANES Data
Dealing with Large Samples
Bubble plots are hard to interpret for large data sets due to overlapping bubbles.
Potential solutions: Create a “sampled scatterplot” in which we
sample from the original data where probability of selection is proportional to sample weights.
“Jitter” the data by adding some random noise to the values before plotting.
These and others discussed in Korn and Graubard (1998).
SAS Code: Plotting a representative subsample
proc surveyselect data=explore.glyco out=plotdata method=pps sampsize=300 seed=3452;
size weight;
run;
symbol1 v=circle i=r c=black ci=green w=2;
proc gplot data=plotdata;
plot glyco*age;
run;
Subsample: Glycohemoglobin vs. Age
Plotting Recommendations
For univariate displays, adjust for the sampling weights.
For scatterplots, sampling weights can be accounted for by using bubble plots.
If the sample is large, a subsampling procedure that incorporates the weights might be more appropriate.
References
Bellhouse ,D.R. and Starfford, J.E. (1999). Density Estimation from complex surveys. Statistica Sinica.
Bellhouse, D. R. and Stafford, J.E. (2001). Local polynomial regression in complex surveys. Survey Methodology.
Bellhouse, D.R. and Stafford, J.E. (2004). Additive models for survey data via penalized least squares. Technical Report.
Buskirk, T.D. and Lohr, S.L. (2005). Asymptotic properties of kernel density estimation with complex survey data. Journal of Statistical Planning and Inference.
Graubard, B.I. and Korn E.L. (2002). Inference for superpopulation parameters using sample surveys. Statistical Science.
Korn, E.L., Midthune, D., and Graubard, B.I. (1997). Estimating interpoloated percentiles from grouped data with large samples. J. Official Statist.
Korn, E.L. and Graubard, B.I. (1998). Scatterplots with survey data. The American Statistician.