In a previous post , Using the Same Sample for Different Models in Stata, we examined how to use the same sample when comparing regression models. Using different samples in our models could lead to erroneous conclusions when interpreting results.
But excluding observations can also result in inaccurate results.
The coefficient for the variable “frequent religious attendance” was negative 58 in model 3 (more…)
One of the most confusing things about mixed models arises from the way it’s coded in most statistical software. Of the ones I’ve used, only HLM sets it up differently and so this doesn’t apply.
But for the rest of them—SPSS, SAS, R’s lme and lmer, and Stata, the basic syntax requires the same pieces of information.
1. The dependent variable
2. The predictor variables for which to calculate fixed effects and whether those (more…)
Fortunately there are some really, really smart people who use Stata. Yes I know, there are really, really smart people that use SAS and SPSS as well.
But unlike SAS and SPSS users, Stata users benefit from the contributions made by really, really smart people. How so? Is Stata an “open source” software package?
Technically a commercial software package (software you have to pay for) cannot be open source. Based on that definition Stata, SPSS and SAS are not open source. R is open source.
But, because I have a Stata license (once you have it, it never expires) I think of Stata as being open source. This is because Stata allows members of the Stata community to share their expertise.
There are countless commands written by very, very smart non-Stata employees that are available to all Stata users.
Practically all of these commands, which are free, can be downloaded from the SSC (Statistical Software Components) archive. The SSC archive is maintained by the Boston College Department of Economics. The website is: https://ideas.repec.org/s/boc/bocode.html
There are over three thousand commands available for downloading. Below I have highlighted three of the 185 that I have downloaded.
1. coefplot is a command written by Ben Jann of the Institute of Sociology, University of Bern, Bern, Switzerland. This command allows you to plot results from estimation commands.
In a recent post on diagnosing missing data, I ran two models comparing the observations that reported income versus the observations that did not report income, models 3d and 3e.
Using the coefplot command I can graphically compare the coefficients and confidence intervals for each independent variable used in the models.
The code and graph are:
coefplot model_3d model_3e, drop(_cons) xline(0)
Including the code xline(0) creates a vertical line at zero which quickly allows me to determine whether a confidence interval spans both positive and negative territory.
I can also separate the predictor variables into individual graphs:
coefplot model_3d || model_3e, yline(0) bycoefs vertical byopts(yrescale) ylabel(, labsize(vsmall))
2. Nicholas Cox of Durham University and Gary Longton of the Fred Hutchinson Cancer Research Center created the command distinct. This command generates a table with the count of distinct observations for each variable in the data set.
When getting to know a data set, it can be helpful to search for potential indicator, categorical and continuous variables. The distinct command along with its min(#) and max(#) options allows an easy search for variables that fit into these categories.
For example, to create a table of all variables with three to seven distinct observations I use the following code:
distinct, min(3) max(7)
In addition, the command generates the scalar r(ndistinct). In the workshop Managing Data and Optimizing Output in Stata, we used this scalar within a loop to create macros for continuous, categorical and indicator variables.
3. In a data set it is not uncommon to have outliers. There are primarily three options for dealing with outliers. We can keep them as they are, winsorize the observations (change their values), or delete them. Note, winsorizing and deleting observations can introduce statistical bias.
If you choose to winsorize your data I suggest you check out the command winsor2. This was created by Lian Yujun of Sun Yat-Sen University, China. This command incorporates coding from the command winsor created by Nicholas Cox and Judson Caskey.
The command creates a new variable, adding a suffix “_w” to the original variable’s name. The default setting changes observations whose values are less than the 1st percentile to the 1 percentile. Values greater than the 99th percentile are changed to equal the 99th percentile. Example:
winsor2 salary (makes changes at the 1st and 99th percentile for the variable “salary”)
The user has the option to change the values to the percentile of their choice.
winsor2 salary, cuts(0.5 99.5) (makes changes at the 0.5st and 99.5th percentile)
To add these three commands to your Stata software execute the following code and click on the links to download the commands:
findit coefplot
findit distinct
findit winsor2
As shown in the December, 2015 free webinar “Stata’s Bountiful Help Resources”, you can also explore all the add-on commands via Stata’s “Help” menu. Go to “Help” => “SJ and User Written Commands” to explore.
Jeff Meyer is a statistical consultant with The Analysis Factor, a stats mentor for Statistically Speaking membership, and a workshop instructor. Read more about Jeff here.
In the last post, we examined how to use the same sample when running a set of regression models with different predictors.
Adding a predictor with missing data causes cases that had been included in previous models to be dropped from the new model.
Using different samples in different models can lead to very different conclusions when interpreting results.
Let’s look at how to investigate the effect of the missing data on the regression models in Stata.
The coefficient for the variable “frequent religious attendance” was negative 58 in model 3 and then rose to a positive 6 in model 4 when income was included. Results (more…)
In our last post, we calculated Pearson and Spearman correlation coefficients in R and got a surprising result.
So let’s investigate the data a little more with a scatter plot.
We use the same version of the data set of tourists. We have data on tourists from different nations, their gender, number of children, and how much they spent on their trip.
Again we copy and paste the following array into R.
M <- structure(list(COUNTRY = structure(c(3L, 3L, 3L, 3L, 1L, 3L, 2L, 3L, 1L, 3L, 3L, 1L, 2L, 2L, 3L, 3L, 3L, 2L, 3L, 1L, 1L, 3L,
1L, 2L), .Label = c("AUS", "JAPAN", "USA"), class = "factor"),GENDER = structure(c(2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L), .Label = c("F", "M"), class = "factor"), CHILDREN = c(2L, 1L, 3L, 2L, 2L, 3L, 1L, 0L, 1L, 0L, 1L, 2L, 2L, 1L, 1L, 1L, 0L, 2L, 1L, 2L, 4L, 2L, 5L, 1L), SPEND = c(8500L, 23000L, 4000L, 9800L, 2200L, 4800L, 12300L, 8000L, 7100L, 10000L, 7800L, 7100L, 7900L, 7000L, 14200L, 11000L, 7900L, 2300L, 7000L, 8800L, 7500L, 15300L, 8000L, 7900L)), .Names = c("COUNTRY", "GENDER", "CHILDREN", "SPEND"), class = "data.frame", row.names = c(NA, -24L))
M
attach(M)
plot(CHILDREN, SPEND)
Let’s use R to explore bivariate relationships among variables.
Part 7 of this series showed how to do a nice bivariate plot, but it’s also useful to have a correlation statistic.
We use a new version of the data set we used in Part 20 of tourists from different nations, their gender, and number of children. Here, we have a new variable – the amount of money they spend while on vacation.
First, if the data object (A) for the previous version of the tourists data set is present in your R workspace, it is a good idea to remove it because it has some of the same variable names as the data set that you are about to read in. We remove A as follows:
rm(A)
Removing the object A ensures no confusion between different data objects that contain variables with similar names.
Now copy and paste the following array into R.
M <- structure(list(COUNTRY = structure(c(3L, 3L, 3L, 3L, 1L, 3L, 2L, 3L, 1L, 3L, 3L, 1L, 2L, 2L, 3L, 3L, 3L, 2L, 3L, 1L, 1L, 3L,
1L, 2L), .Label = c("AUS", "JAPAN", "USA"), class = "factor"),GENDER = structure(c(2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L), .Label = c("F", "M"), class = "factor"), CHILDREN = c(2L, 1L, 3L, 2L, 2L, 3L, 1L, 0L, 1L, 0L, 1L, 2L, 2L, 1L, 1L, 1L, 0L, 2L, 1L, 2L, 4L, 2L, 5L, 1L), SPEND = c(8500L, 23000L, 4000L, 9800L, 2200L, 4800L, 12300L, 8000L, 7100L, 10000L, 7800L, 7100L, 7900L, 7000L, 14200L, 11000L, 7900L, 2300L, 7000L, 8800L, 7500L, 15300L, 8000L, 7900L)), .Names = c("COUNTRY", "GENDER", "CHILDREN", "SPEND"), class = "data.frame", row.names = c(NA, -24L))
M
attach(M)
Do tourists with greater numbers of children spend more? Let’s calculate the correlation between CHILDREN and SPEND, using the cor() function.
R <- cor(CHILDREN, SPEND)
[1] -0.2612796
We have a weak correlation, but it’s negative! Tourists with a greater number of children tend to spend less rather than more!
(Even so, we’ll plot this in our next post to explore this unexpected finding).
We can round to any number of decimal places using the round() command.
round(R, 2)
[1] -0.26
The percentage of shared variance (100*r2) is:
100 * (R**2)
[1] 6.826704
To test whether your correlation coefficient differs from 0, use the cor.test() command.
cor.test(CHILDREN, SPEND)
Pearson's product-moment correlation
data: CHILDREN and SPEND
t = -1.2696, df = 22, p-value = 0.2175
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.6012997 0.1588609
sample estimates:
cor
-0.2612796
The cor.test() command returns the correlation coefficient, but also gives the p-value for the correlation. In this case, we see that the correlation is not significantly different from 0 (p is approximately 0.22).
Of course we have only a few values of the variable CHILDREN, and this fact will influence the correlation. Just how many values of CHILDREN do we have? Can we use the levels() command directly? (Recall that the term “level” has a few meanings in statistics, once of which is the values of a categorical variable, aka “factor“).
levels(CHILDREN)
NULL
R does not recognize CHILDREN as a factor. In order to use the levels() command, we must turn CHILDREN into a factor temporarily, using as.factor().
levels(as.factor(CHILDREN))
[1] "0" "1" "2" "3" "4" "5"
So we have six levels of CHILDREN. CHILDREN is a discrete variable without many values, so a Spearman correlation can be a better option. Let’s see how to implement a Spearman correlation:
cor(CHILDREN, SPEND, method ="spearman")
[1] -0.3116905
We have obtained a similar but slightly different correlation coefficient estimate because the Spearman correlation is indeed calculated differently than the Pearson.
Why not plot the data? We will do so in our next post.
About the Author: David Lillis has taught R to many researchers and statisticians. His company, Sigma Statistics and Research Limited, provides both on-line instruction and face-to-face workshops on R, and coding services in R. David holds a doctorate in applied statistics.
See our full R Tutorial Series and other blog posts regarding R programming.