chapter 5-9: missing data imputation

Chapter 5-9. Missing Data Imputation

In this chapter we will discuss what to do about missing data, and particularly the imputation schemes available in Stata.

To offer a “precise” definition,

Missing data imputation is substituting values for missing values—but it is not fabricating data because we do it statistically.

Although you rarely see authors describe how they handled missing data in their articles, it is becoming common to find entire chapters on this subject in statistical textbooks. For example, such chapters can be found in Harrell (2001, pp.41-52), Twisk (2003, pp.202-224), and Fleiss et al. (2003, pp. 491-560).

Listwise Deletion

Stata, like other statistical software, uses listwise deletion of missing values, which can diminish the sample size very quickly in regression models. With listwise deletion, a subject is dropped from the analysis if it is missing at least one of the variables used in the model (y, x1, or x2) in the following example.

Consider the following dataset.

. list +---------------------------------+ | id y x1 x2 x3 s x4 | |---------------------------------| 1. | 1 11 1 2 3 a . | 2. | 2 10 . 5 . b 5 | 3. | 3 5 3 2 4 3 | 4. | 4 9 . . 5 c 1 | 5. | 5 12 5 7 1 d 2 | |---------------------------------| 6. | 6 7 6 3 2 e 5 | +---------------------------------+

Ignoring obvious overfitting for sake of illustration, the following regression command will lose two subjects from the sample size due to listwise deletion of missing data.

_________________ Source: Stoddard GJ. Biostatistics and Epidemiology Using Stata: A Course Manual. Salt Lake City, UT: University of Utah School of Medicine. Chapter 5-9. (Accessed February 15, 2012, at http://www.ccts.utah.edu/biostats/ ?pageId=5385).

Chapter 5-9 (revision 15 Feb 2012) p. 1

. regress y x1 x2

Source | SS df MS Number of obs = 4-------------+------------------------------ F( 2, 1) = 1.16 Model | 22.8676471 2 11.4338235 Prob > F = 0.5493 Residual | 9.88235294 1 9.88235294 R-squared = 0.6982-------------+------------------------------ Adj R-squared = 0.0947 Total | 32.75 3 10.9166667 Root MSE = 3.1436

------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- x1 | -1 .9701425 -1.03 0.490 -13.32683 11.32683 x2 | 1.352941 .9036642 1.50 0.375 -10.1292 12.83508 _cons | 7.764706 3.654641 2.12 0.280 -38.67191 54.20132------------------------------------------------------------------------------

_________________ Source: Stoddard GJ. Biostatistics and Epidemiology Using Stata: A Course Manual [unpublished manuscript] University of Utah School of Medicine, 2011. http://www.ccts.utah.edu/biostats/?pageId=5385

We just lost 1/3 of our sample (n=4 instead of n=6). That may seriously bias the results, not to mention the loss of statistical power.

Although it is what most researchers do, just dropping subjects from the analysis that have at least one missing value for the variable in the model, or listwise deletion of missing data, results in regression coefficients that can be terribly biased, imprecise, or both (Harrell, 2001, pp.43-44).

Types of Missing Data

Harrell (2001, pp.41-52) discusses three types of missing data.

Missing completely at random (MCAR) Data are missing for reasons unrelated to any characteristics or responses of the subject, including the value of the missing value, were it to be known. An example is the accidental dropping of test tube resulting in missing laboratory measurements. (Here, the best guess of the missing variable is simply the sample median).

Missing at random (MAR) Data elements are not missing at random, but the probability that a value is missing depends on values of variables that were actually measured. For example, suppose males are less likely to respond to their income question in general, but the likelihood of responding is independent of their actual income. In this case, unbiased sex-specific income estimates can be made if we have data on the sex variable (by replacing the missing value with the sex-specific median income, for example).

Informative missing (IM) Data elements are more likely to be missing if their true values of the variable in question are systematically higher or lower. For example, this occurs if lower income subjects, or high income subjects, or both, are less likely to answer the income question in a survey. This is the most difficult type of missing data to handle, and in many cases there is


no good value to substitute for the missing value. Furthermore, if you analyze your data by just dropping these subjects, your results will be biased, so that does not work either.

Missing Comorbidities In Patient Medical Record

A special case of missing is a comorbidity that is not listed in the patient’s medical record. For example, if no mention of diabetes was ever made and a diagnostic code for diabetes was never entered for any clinic visit, the fact that it is missing suggests that the patient does not have diabetes. Defining a coding rule to replace this missing value with 0, or absent, will most likely produce the least amount of misclassification error.

Steyerberg (2009, p.130-131) mentions this approach, “An alternative in such a situation might be to change the definition of the predictor, i.e., by assuming that if no value is available from a patient chart, the characteristic is absent rather than missing.”

Replacing Missing Values with Mean, Median, or Mode

Before the more sophisticated imputation schemes were developed, it was common practice to replace the missing value with a likely value, being the mean, median, or mode.

One criticism of this approach is that you artificially shrink the variance, since so many observations will now have the average value.

Royston (2004) makes this criticism,

“Old-fashioned imputation typically replaced missing values with the mean or mode of the nonmissing values for that variable. That approach is now regarded as inadequate. For subsequent statistical inference to be valid, it is essential to inject the correct degree of randomness into the imputations and to incorporate that uncertainty when computing standard errors and confidence intervals for parameters of interest.”

One possible approach is imputing the missing value with a likely value, such as the median. Then, add a random residual back to the median imputed value to maintain the correct standard error (Harrell, 2001, pp.45-46).

Such a direct approach is not usually done, however, since the more widely accepted approaches, accomplish the same thing. Furthermore, if there are a lot of missing data, imputing with a likely value might adversely affect the regression coefficient. The imputation methods of multiple imputation and maximum likelihood not only provide the best standard errors, but also the best regression coefficients.


What About Imputing the Outcome Variable?

It is common to discard subjects with a missing outcome variable, but imputing missing values of the outcome variable frequently leads to more efficient estimates of the regression coefficients when the imputation is based on the nonmissing predictor variables (Harrell, 2001, p.43).

Missing Value Indicator Approach

A historically popular approach in epidemiologic research was to use a missing value indicator, which has a value of 1 if the variable is missing and 0 otherwise.

For example, given the following variable for gender,

1. male n = 502. female n = 40

Missing n = 10

we would recode this to two indicators, male and malemissing:

Original gender variable

Male indicator

Malemissingindicator

1. male (n=50) 1 (n=50) 0 (n=50)2. female (n=40) 0 (n=40) 0 (n=40). = missing (n=10) 0 (n=10) 1 (n=10)

and then include both indicator variables into the regression model. With this approach, the missing value indicator is not interpreted, or reported in an article, but simply acts as a place holder so the subjects with missing values are not dropped out of the analysis.

Greenland and Finkle (1995) suggest not using the missing value indictor approach,

“Epidemiologic studies often encounter missing covariate values. While simple methods such as stratification on missing-data status, conditional-mean imputation, and complete-subject analysis are commonly employed for handling this problem, several studies have shown that these methods can be biased under reasonable circumstances. The authors review these results in the context of logistic regression and present simulation

experiments showing the limitations of the methods. The method based on missing-data indicators can exhibit severe bias even when the data are missing completely at random, and regression (conditional-mean) imputation can be inordinately sensitive to model misspecification. Even complete-subject analysis can outperform these methods. More sophisticated methods, such as maximum likelihood, multiple imputation, and weighted

estimating equations, have been given extensive attention in the statistics literature. While these methods are superior to simple methods, they are not commonly used in epidemiology, no doubt due to their complexity and the lack of packaged software to apply these methods. The authors contrast the results of multiple imputation to simple methods in the analysis of a case-control study of endometrial cancer, and they find a


meaningful difference in results for age at menarche. In general, the authors recommend that epidemiologists avoid using the missing-indicator method and use more sophisticated methods whenever a large proportion of data are missing.”

Huberman and Langholz (1999) later proposed the missing value indicator approach for matched case-control studies, which was not specifically discussed in the Greenland and Finke paper. Li et al (2004) criticized the Huberman and Langholz proposal, stating that the approach does not perform as well as Huberman and Langholz suggested.

Steyerberg (2009, pp.130-131) likewise advises not using the missing value indicator approach,

“…such a procedure ignores correlation of the values of predictors among each other. Simulations have shown that the procedure may lead to severe bias in estimated regression coefficients.155,295. The missing indicator should hence generally not be used.”-----155Greenland S, Finkle WD. A critical look at methods for handling missing covariates in

epidemiologic regression analysis. Am J Epidemiol 1995;142(12):1255-64.295Moons KG, Grobbee DE. Diagnostic studies as multivariable, prediction research. J

Epidemiol Community Health 2002;56(5):337-8.

Hotdeck Imputation (command “hotdeck”, contributed by Mander and Clayton)

With hot deck imputation, each missing value is replaced with the value from the most similar case for which the variable is not missing.

Hotdeck imputation is available in Stata, which requires you to update your Stata to get the command hotdeck, but instead of replacing only the missing values, it replaces the entire observation with an observation that has no missing data. Thus, both missing and nonmissing variables for a subject are replaced, which does not seem very appealing. In addition, the replacement is not with the most similar observation, which is the most appealing feature of hotdeck imputation, but instead the replacement is with a random observation.

Royston (2004) criticizes the method,

“Hotdeck imputation was implemented in Stata in 1999 by Mander and Clayton. However, this technique may perform poorly when many rows of data have at least one missing value.”


Hotdeck Imputation (command “hotdeckvar”, contributed by Schonlau)

A better version of hotdeck is available on the Internet. Schonlau developed a Stata procedure to perform a simple hotdeck imputation. Missing values are replaced by random values from the same variable. Although this is not the “most similar case”, which true hotdeck imputation is supposed to achieve, it is intuitively more appealing than the Mander and Clayton procedure.

Schonlau’s version can be found on his website (http://www.schonlau.net/statasoftware.html).

To install it, connect to the Internet and enter the following commands in the Stata Command Window:

net from http://www.schonlau.net/statanet install hotdeckvar

and then click on the “hotdeckvar” link.

To get help for this in Stata enter

help hotdeckvar

Article Statistical Methods Suggestion For Schonlau’s Hotdeck Imputation

If you wanted to use hotdeck imputation, you could use the following in your Statistical Methods section:

Imputation for missing values was performed using the hotdeck procedure, where missing values were replaced by random values from the same variable, using the Schonlau implementation for the Stata software (Schonlau, 2006). Hotdeck imputation has the advantage of being simple to use, it preserves the distributional characteristics of the variable, and performs nearly as well as the more sophisticated imputation approaches (Roth, 1994).

Multiple Imputation

An excellent website discussing multiple imputation is: http://www.multiple-imputation.com/, and then click on the What is MI? link. This website was created by S. van Buuren, one of the authors of the MICE method (Multiple Imputation by Chained Equations). The multiple imputation routine available in Stata uses the MICE method.

Multiple imputation was implemented in Stata by Royston (2004). It was updated by Royston (2005a), then updated again by Royston (2005b), and again by Royston (2007), and again by Carlin, Galati, and Royston (2008), and so on….


http://www.multiple-imputation.com/

Royston (2004) describes the method:

“This article describes an implementation for Stata of the MICE method of multiplemultivariate imputation described by van Buuren, Boshuizen, and Knook (1999).MICE stands for multivariate imputation by chained equations. The basic idea ofdata analysis with multiple imputation is to create a small number (e.g., 5–10)of copies of the data, each of which has the missing values suitably imputed, andanalyze each complete dataset independently. Estimates of parameters of interestare averaged across the copies to give a single estimate. Standard errors arecomputed according to the “Rubin rules”, devised to allow for the between- andwithin-imputation components of variation in the parameter estimates.”

This is the best imputation approach available in Stata, and so is the recommended approach if the proportion of missing data is greater than 5% (see Harrell guideline below). If you use it and want to say you did in your article, you would report it as:

Article Statistical Methods Section Suggestion

If you wanted to use multiple imputation, you could use the following in your Statistical Methods section:

Missing data were imputed using the method of multiple multivariate imputation described by van Buuren, et al (1999) as implemented in the STATA software (Royston, 2004).

We will practice with this method below.

The Stata commands for multiple imputation assume data to be missing at random (MAR) or missing completely at random (MCAR).

Exercise: Look at the Vandenbrouchke et al (2007) STROBE statement suggestion for reporting your missing value imputation approach.

On page W-176 under the heading “12(c) Explain how missing data were addressed”, they give an example description for your Statistical Methods section, an explanation, and in Box 6 on the next page, W-177, they give details about imputation in general, which are consistent with the presentation in this chapter.

They give this example (a clinical paper, their reference 106) for explaining in your manuscript how imputation was done,

“Our missing data analysis procedures used missing at random (MAR) assumptions. We used the MICE (multivariate imputation by chained equations) method of multiple


multivariate imputation in STATA. We independently analyzed 10 copies of the data, each with missing values suitably imputed , in the multivariate logistic regression analyses. We average estimates of the variables to give a single mean estimate and adjusted standard errors according to Rubin’s rules” (106).------- 106. Chandola T, Brunner E, Marmot M. Chronic stress at work and themetabolic syndrome: prospective study. BMJ 2006;332:521-5. PMID:16428252

This paragraph is very similar to the Royston (2004) description on the previous page.

Some Crude Guidelines

Harrell provides these crude guidelines (2001, p.49):

“Proportion of missings 0.05: It doesn’t matter very much how you impute missings or whether you adjust variance of regression coefficient estimates for having imputed data in this case. For continuous variables imputing missings with the median nonmissing value is adequate; for categorical predictors the most frequent category can be used. Complete case analysis is an option here.”

“Proportion of missings 0.05 to 0.15: If a predictor is unrelated to all of the other predictors, imputations can be done the same as the above (i.e., impute a reasonable constant value). If the predictor is correlated with other predictors, develop a customized model (or have the transcan fuction [available for S-Plus from Harrell’s website] do it for you) to predict the predictor from all of the other predictors. Then impute missings with predicted values. For categorical variables, classification trees are good methods for developing customized imputation models. For continuous variables, ordinary regression can be used if the variable in question does not require a nonmonotonic transformation to be predicted from the other variables. For either the related or unrelated predictor case, variances may need to adjusted for imputation. Single imputation is probably OK here, but multiple imputation doesn’t hurt.”

“Proportion of missings > 0.15: This situation requires the same considerations as in the previous case, and adjusting variances for imputation is even more important. To estimate the strength of the effect of a predictor that is frequently missing, it may be necessary to refit the model on the subject of observations for which that predictor is not missing, if Y is not used for imputation. Multiple imputation is preferred for most models.”


Counting Number of Missing Values

A quick way to see how many missing values you have in your variables is to use the nmissing or npresent commands.

First, you have to update your Stata to add them, which you can do with the following command while connected to the Internet.

findit nmissing

SJ-5-4 dm67_3 . . . . . . . . . . Software update for nmissing and npresent (help nmissing if installed) . . . . . . . . . . . . . . . N. J. Cox Q4/05 SJ 5(4):607 now produces saved results

Click on the dm67_3 link to install, which gives you:

INSTALLATION FILES (click here to install) dm67_3/nmissing.ado dm67_3/nmissing.hlp dm67_3/npresent.ado dm67_3/npresent.hlp

and then click on the “(click here to install)” link.

Having done that, you can use the following to see the number of missing values for each variable:

nmissing

Alternatively, you can using the following to see the number of nonmissing vaues for each variable:

npresent


Stata Practice Imputing with Likely Value

Bringing in some data to practice with

File Open Find the directory where you copied the CD Change to the subdirectory datasets & do-files Single click on births_with_missing.dta

Open

use "C:\Documents and Settings\u0032770.SRVR\Desktop\ Biostats & Epi With Stata\datasets & do-files\ births_with_missing.dta", clear

* which must be all on one line, or use: cd "C:\Documents and Settings\u0032770.SRVR\Desktop\"cd "Biostats & Epi With Stata\datasets & do-files" use births_with_missing, clear

Looking at the data

sum

Variable | Obs Mean Std. Dev. Min Max-------------+-------------------------------------------------------- id | 500 250.5 144.4818 1 500 bweight | 478 3137.253 637.777 628 4553 lowbw | 478 .1213389 .3268628 0 1 gestwks | 447 38.79617 2.14174 26.95 43.16 preterm | 447 .1230425 .328854 0 1-------------+-------------------------------------------------------- matage | 485 34.05979 3.905724 23 43 hyp | 478 .1401674 .3475243 0 1 sex | 459 1.479303 .5001165 1 2 sexalph | 0

We have (500-478)/500, or 4.4% missing for that dichotomous variable hyp. Using Harrell’s guideline for proportion missing 5%, we can simply impute those missings with the modal value of the variable.


Here we might use a naming convention of “nm” for “no missing” prefixed onto the variable name, so that we can easily recognize the original variable and the imputed variable.

capture drop nmhyptab hyp // look at output to see that modal value is 0gen nmhyp=hypreplace nmhyp=0 if hyp==.tab nmhyp hyp , missing

. tab hyp

hypertens | Freq. Percent Cum.------------+----------------------------------- 0 | 411 85.98 85.98 1 | 67 14.02 100.00------------+----------------------------------- Total | 478 100.00

. tab nmhyp hyp , missing

| hypertens nmhyp | 0 1 . | Total-----------+---------------------------------+---------- 0 | 411 0 22 | 433 1 | 0 67 0 | 67 -----------+---------------------------------+---------- Total | 411 67 22 | 500

Alternatively, to make your do-file more automated, so that you don’t have to change these lines everytime you add new subjects to your dataset, you could use:

capture drop nmhypgen nmhyp=hypcount if hyp==0 // returns the #0's in r(N)scalar count0=r(N) // store #0’s in count0count if hyp==1 // returns the #1's in r(N)scalar count1=r(N) // store #1’s in count1replace nmhyp =0 if (hyp ==.) & (count0>=count1)replace nmhyp =1 if (hyp ==.) & (count0<count1)tab nmhyp hyp , missing

Here, we used the count command to count the number of occurrences of 0 and 1 and stored these in scalars (variables with one element). Then we imputed with the most frequent category.

. tab nmhyp hyp , missing

| hypertens nmhyp | 0 1 . | Total-----------+---------------------------------+---------- 0 | 411 0 22 | 433 1 | 0 67 0 | 67 -----------+---------------------------------+---------- Total | 411 67 22 | 500

For the continuous variable matage, we have (500-485)/500, or 3% missing. Using Harrell’s guideline for proportion missing 5%, we can simply impute those missings with the median of the variable. We can use either of the following two commands to discover the median.Chapter 5-9 (revision 15 Feb 2012)

p. 11

centile matage, centile(50)sum matage, detail

. centile matage, centile(50)

-- Binom. Interp. -- Variable | Obs Percentile Centile [95% Conf. Interval]-------------+------------------------------------------------------------- matage | 485 50 34 34 35

. sum matage, detail

maternal age------------------------------------------------------------- Percentiles Smallest 1% 25 23 5% 27 2410% 29 25 Obs 48525% 31 25 Sum of Wgt. 485

50% 34 Mean 34.05979 Largest Std. Dev. 3.90572475% 37 4290% 39 43 Variance 15.2546895% 40 43 Skewness -.24138199% 42 43 Kurtosis 2.483957

To impute with the median of 34, we could use

capture drop nmmatage gen nmmatage=matagereplace nmmatage=34 if matage==.sum nmmatage

Variable | Obs Mean Std. Dev. Min Max-------------+-------------------------------------------------------- nmmatage | 500 34.058 3.846587 23 43

Alternatively, to make your do-file more automated, so that you don’t have to change these lines everytime you add new subjects to your dataset, you could use:

capture drop nmmatage gen nmmatage=matagesum matage, detail*return list // to discover median is r(p50)replace nmmatage=r(p50) if matage==. sum nmmatage

After running the sum command, followed by “return list” without the “*”, where it was discovered that the median is stored in the macro name r(p50), we can simply delete the return list line, or comment it out using the asterick.


Suppose the missing data are the Missing at random (MAR) case (see page 2). A better “likely value” can be obtained with regression.

For the gestwks variable, there are (500-447)/500, or 10.6% missing. Although multiple imputation would be better, since it adjusts the variability, let’s try the regression approach just to see how it works. Later on, we will compare the result to multiple imputation.

To find out what other predictors are correlated with gestwks, we can use

corr bweight-sex

| bweight lowbw gestwks preterm matage hyp sex-------------+--------------------------------------------------------------- bweight | 1.0000 lowbw | -0.7083 1.0000 gestwks | 0.6969 -0.6045 1.0000 preterm | -0.5580 0.5653 -0.7374 1.0000 matage | 0.0260 -0.0268 0.0335 -0.0039 1.0000 hyp | -0.1923 0.1297 -0.1796 0.1297 -0.0527 1.0000 sex | -0.1654 0.0661 -0.0397 0.0500 -0.0351 -0.0771 1.0000

We see that lowbw, preterm, hyp, and sex are correlated with gestwks. Using Stata’s impute command,

capture drop nmgestwksimpute gestwks lowbw preterm hyp sex , gen(nmgestwks)sum gestwks nmgestwks

We see that the imputed variable has a mean very similar to the original variable, but that the standard deviation is smaller.

Variable | Obs Mean Std. Dev. Min Max-------------+-------------------------------------------------------- gestwks | 447 38.79617 2.14174 26.95 43.16 nmgestwks | 500 38.78908 2.082616 26.95 43.16

This always happens, and is why we find the phrase “variances may need to adjusted for imputation” in Harrell’s “Proportion of missings 0.05 to 0.15” rule above. The diminished variance may lead to erroneous statistical significance. The impute command does not add back in random variability to the imputed values.


Stata Practice Imputing with Hotdeck Imputation

First, we must update our Stata to include hotdeck imputation, as was done on Page 5, if we did not do this yet.

net from http://www.schonlau.net/statanet install hotdeckvar

We will use a small dataset so we can keep track of what is happening.

use births_miss_small, clearlist +-----------------------------------------+ | id bweight lowbw gestwks matage | |-----------------------------------------| 1. | 1 2620 0 38.15 35 | 2. | 2 3751 0 39.8 31 | 3. | 3 3200 0 38.89 33 | 4. | 4 3673 0 . . | 5. | 5 . . 38.97 35 | |-----------------------------------------| 6. | 6 3001 0 41.02 38 | 7. | 7 1203 1 . . | 8. | 8 3652 0 . . | 9. | 9 3279 0 39.35 30 | 10. | 10 3007 0 . . | |-----------------------------------------| 11. | 11 2887 0 38.9 28 | 12. | 12 . . 40.03 27 | 13. | 13 3375 0 . 36 | 14. | 14 2002 1 36.48 37 | 15. | 15 2213 1 37.68 39 | +-----------------------------------------+

To see the help for hotdeckvar, use

help hotdeckvar


To impute all the missing values in this dataset, we use the following. We first set the seed to the random number generator so that we get the same imputed values each time we run the hotdeckvar command.

set seed 999 // otherwise imputed variables change hotdeckvar bweight lowbw gestwks matage, suffix("_hot")list bweight_hot-matage_hot, abbrev(15)

+----------------------------------------------------+ | bweight_hot lowbw_hot gestwks_hot matage_hot | |----------------------------------------------------| 1. | 2620 0 38.15 35 | 2. | 3751 0 39.8 31 | 3. | 3200 0 38.89 33 | 4. | 3673 0 37.68 39 | 5. | 2620 0 38.97 35 | |----------------------------------------------------| 6. | 3001 0 41.02 38 | 7. | 1203 1 39.8 31 | 8. | 3652 0 38.89 33 | 9. | 3279 0 39.35 30 | 10. | 3007 0 41.02 38 | |----------------------------------------------------| 11. | 2887 0 38.9 28 | 12. | 3200 0 40.03 27 | 13. | 3375 0 39.8 36 | 14. | 2002 1 36.48 37 | 15. | 2213 1 37.68 39 | +----------------------------------------------------+

For analysis, we simply use these new imputed variables.


Stata Practice Imputing with Multiple Imputation

A significant improvement was made to multiple imputation in Stata version 11. There is now a Stata manual, Multiple Imputation, available. To see it, click on Help on the Stata menu bar, then click on PDF Documentation. It is all done with the mi command.

The Version 11 commands did not fill in the missing values as well, but the Version 10 approach obtained an estimate for each missing value.

Version 10: Multiple Imputation

If you have Stata Version 11, do not do this section. Just look at the process it went through, and then go on to the Version 11 section.

First, we must update our Stata to include the multiple imputation commands: ice and micombine. Use

findit ice

which takes you to a help screen where several versions of these commands are:

First, click on the st0067_3 link:

SJ-7-4 st0067_3 . . . . Multiple imputation of missing values: Update of ice (help ice, ice_reformat, micombine, uvis if installed) . . P. Royston Q4/07 SJ 7(4):445--464 update of ice allowing imputation of left-, right-, or interval-censored observations

which brings up the following:

INSTALLATION FILES (click here to install) st0067_3/ice.ado st0067_3/ice.hlp st0067_3/ice_reformat.ado st0067_3/ice_reformat.hlp st0067_3/micombine.ado st0067_3/micombine.hlp st0067_3/uvis.ado st0067_3/uvis.hlp st0067_3/cmdchk.ado st0067_3/nscore.ado

Second, click on the click here to install link:


Third, click on the st0067_4 link:

SJ-9-3 st0067_4 . Mult. imp.: update of ice, with emphasis on cat. variables (help ice, uvis if installed) . . . . . . . . . . . . . . . P. Royston Q3/09 SJ 9(3):466--477 update of ice package with emphasis on categorical variables; clarifies relationship between ice and mi

which brings up the following:

INSTALLATION FILES (click here to install) st0067_4/ice.ado st0067_4/ice.hlp st0067_4/ice_.ado st0067_4/uvis.ado st0067_4/uvis.hlpfollowed by clicking on the “(click here to to install)” link.

Fourth, click on the click here to install link:

In this chapter, the ice and micombine commands are used. The multiple imputation procedure for Stata version 10 was later updated to include the mim and mimstack commands. The old commands seemed easier to use, and should give the same result, so this chapter still teaches the ice and micombine commands.

Again, we will use a small dataset so we can keep track of what is happening.

use births_miss_small, clearlist

+-----------------------------------------+ | id bweight lowbw gestwks matage | |-----------------------------------------| 1. | 1 2620 0 38.15 35 | 2. | 2 3751 0 39.8 31 | 3. | 3 3200 0 38.89 33 | 4. | 4 3673 0 . . | 5. | 5 . . 38.97 35 | |-----------------------------------------| 6. | 6 3001 0 41.02 38 | 7. | 7 1203 1 . . | 8. | 8 3652 0 . . | 9. | 9 3279 0 39.35 30 | 10. | 10 3007 0 . . | |-----------------------------------------| 11. | 11 2887 0 38.9 28 | 12. | 12 . . 40.03 27 | 13. | 13 3375 0 . 36 | 14. | 14 2002 1 36.48 37 | 15. | 15 2213 1 37.68 39 | +-----------------------------------------+

The stata commands we will use are explain fully in the Royston (2005a, 2005b, 2007) articles, which are updated versions of the routines explained fully in the Royston (2004) article. These articles, as with any Stata Journal article that is at least two years old, can be downloaded at no cost from the Stata Corporation website, if you want them. More recent articles must be paid for.


http://www.stata-journal.com/archives.html


With listwise deletion of missing values, we get the following linear regression.

regress bweight gestwks matage


------------------------------------------------------------------------------ bweight | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- gestwks | 274.9777 83.99418 3.27 0.022 59.06382 490.8916 matage | -66.55269 28.83879 -2.31 0.069 -140.6852 7.57979 _cons | -5541.07 3641.212 -1.52 0.189 -14901.1 3818.962------------------------------------------------------------------------------

van Buuren (1999, p.686) describes the multiple imputation method:

“Multiple imputation will be applied to account for the non-response. The main tasks to be accomplished in multiple imputation are:1. Specify the posterior predictive density p(Ymis|X,R), where X is a set of predictor variables, given the non-response mechanism p(R|Y,Z) and the complete data model p(Y,Z).2. Draw imputations from this density to produce m complete data sets.3. Perform m complete-data analyses (Cox regression in our case) on each completed data matrix.4. Pool the m analyses results into final point and variance estimates. Simulation studies have shown that the required number of repeated imputations m can be as low as three for data with 20 per cent of missing entries.10 In the following we use m=5, which is a conservative choice.”

Next we will obtain the multiple imputation solution. First we use the mvis command, which imputes missing values in the mainvarlist m times by using “switching regression”, an iterative multivariate regression technique. The imputed and non-imputed variables are stored in a new file called filename.dta.

The syntax is:

ice mainvarlist [if] [in] [weight] [, boot [(varlist)]cc(ccvarlist) cmd(cmdlist) cycles(#) dropmissing dryrun eq(eqlist) genmiss(string) id(string) m(#) interval(intlist) match[(varlist)]noconstant nopp noshoweq nowarning on(varlist) orderasis passive(passivelist) replace saving(filename [, replace]) seed(#) substitute(sublist) trace(filename)


We use

ice bweight gestwks matage , m(5) genmiss(nm) /// saving(bwtimp, replace) seed(888)

To see what this did, we can use

use bwtimp, clearlist

+----------------------------------------------------------------------------------------+ | id bweight lowbw gestwks matage _mi _mj nmbwei~t nmgest~s nmmatage | |----------------------------------------------------------------------------------------| 1. | 1 2620 0 38.15 35 1 0 . . . | 2. | 2 3751 0 39.8 31 2 0 . . . | 3. | 3 3200 0 38.89 33 3 0 . . . | 4. | 4 3673 0 . . 4 0 . . . | 5. | 5 . . 38.97 35 5 0 . . . | |----------------------------------------------------------------------------------------| 6. | 6 3001 0 41.02 38 6 0 . . . | 7. | 7 1203 1 . . 7 0 . . . | 8. | 8 3652 0 . . 8 0 . . . | 9. | 9 3279 0 39.35 30 9 0 . . . | 10. | 10 3007 0 . . 10 0 . . . | |----------------------------------------------------------------------------------------| 11. | 11 2887 0 38.9 28 11 0 . . . | 12. | 12 . . 40.03 27 12 0 . . . | 13. | 13 3375 0 . 36 13 0 . . . | 14. | 14 2002 1 36.48 37 14 0 . . . | 15. | 15 2213 1 37.68 39 15 0 . . . | |----------------------------------------------------------------------------------------| 16. | 1 2620 0 38.15 35 1 1 0 0 0 | 17. | 2 3751 0 39.8 31 2 1 0 0 0 | 18. | 3 3200 0 38.89 33 3 1 0 0 0 | 19. | 4 3673 0 39.035 30.4696 4 1 0 1 1 | 20. | 5 2573.08 . 38.97 35 5 1 1 0 0 | |----------------------------------------------------------------------------------------| 21. | 6 3001 0 41.02 38 6 1 0 0 0 | 22. | 7 1203 1 37.32458 38.3812 7 1 0 1 1 | 23. | 8 3652 0 40.36074 30.7336 8 1 0 1 1 | 24. | 9 3279 0 39.35 30 9 1 0 0 0 | 25. | 10 3007 0 38.58094 35.3263 10 1 0 1 1 | |----------------------------------------------------------------------------------------| 26. | 11 2887 0 38.9 28 11 1 0 0 0 | 27. | 12 3678.1 . 40.03 27 12 1 1 0 0 | 28. | 13 3375 0 40.13427 36 13 1 0 1 0 | 29. | 14 2002 1 36.48 37 14 1 0 0 0 | 30. | 15 2213 1 37.68 39 15 1 0 0 0 | |----------------------------------------------------------------------------------------| 31. | 1 2620 0 38.15 35 1 2 0 0 0 | 32. | 2 3751 0 39.8 31 2 2 0 0 0 | 33. | 3 3200 0 38.89 33 3 2 0 0 0 | 34. | 4 3673 0 39.02037 28.6181 4 2 0 1 1 | 35. | 5 2663.96 . 38.97 35 5 2 1 0 0 | |----------------------------------------------------------------------------------------| 36. | 6 3001 0 41.02 38 6 2 0 0 0 | 37. | 7 1203 1 36.64371 39.5586 7 2 0 1 1 | 38. | 8 3652 0 39.96529 32.5712 8 2 0 1 1 | 39. | 9 3279 0 39.35 30 9 2 0 0 0 | 40. | 10 3007 0 39.37796 31.3312 10 2 0 1 1 | |----------------------------------------------------------------------------------------| 41. | 11 2887 0 38.9 28 11 2 0 0 0 | 42. | 12 3949.46 . 40.03 27 12 2 1 0 0 | 43. | 13 3375 0 40.42688 36 13 2 0 1 0 | 44. | 14 2002 1 36.48 37 14 2 0 0 0 | 45. | 15 2213 1 37.68 39 15 2 0 0 0 | |----------------------------------------------------------------------------------------| 46. | 1 2620 0 38.15 35 1 3 0 0 0 |


47. | 2 3751 0 39.8 31 2 3 0 0 0 | 48. | 3 3200 0 38.89 33 3 3 0 0 0 | 49. | 4 3673 0 40.09019 22.9542 4 3 0 1 1 | 50. | 5 2521.11 . 38.97 35 5 3 1 0 0 | |----------------------------------------------------------------------------------------| 51. | 6 3001 0 41.02 38 6 3 0 0 0 | 52. | 7 1203 1 35.87934 42.478 7 3 0 1 1 | 53. | 8 3652 0 41.6578 34.7143 8 3 0 1 1 | 54. | 9 3279 0 39.35 30 9 3 0 0 0 | 55. | 10 3007 0 41.21783 42.4263 10 3 0 1 1 | |----------------------------------------------------------------------------------------| 56. | 11 2887 0 38.9 28 11 3 0 0 0 | 57. | 12 3544.44 . 40.03 27 12 3 1 0 0 | 58. | 13 3375 0 41.06176 36 13 3 0 1 0 | 59. | 14 2002 1 36.48 37 14 3 0 0 0 | 60. | 15 2213 1 37.68 39 15 3 0 0 0 | |----------------------------------------------------------------------------------------| 61. | 1 2620 0 38.15 35 1 4 0 0 0 | 62. | 2 3751 0 39.8 31 2 4 0 0 0 | 63. | 3 3200 0 38.89 33 3 4 0 0 0 | 64. | 4 3673 0 39.85606 25.5008 4 4 0 1 1 | 65. | 5 3028.08 . 38.97 35 5 4 1 0 0 | |----------------------------------------------------------------------------------------| 66. | 6 3001 0 41.02 38 6 4 0 0 0 | 67. | 7 1203 1 33.76732 29.3472 7 4 0 1 1 | 68. | 8 3652 0 41.02277 31.6178 8 4 0 1 1 | 69. | 9 3279 0 39.35 30 9 4 0 0 0 | 70. | 10 3007 0 37.80869 17.7524 10 4 0 1 1 | |----------------------------------------------------------------------------------------| 71. | 11 2887 0 38.9 28 11 4 0 0 0 | 72. | 12 3761.25 . 40.03 27 12 4 1 0 0 | 73. | 13 3375 0 38.98916 36 13 4 0 1 0 | 74. | 14 2002 1 36.48 37 14 4 0 0 0 | 75. | 15 2213 1 37.68 39 15 4 0 0 0 | |----------------------------------------------------------------------------------------| 76. | 1 2620 0 38.15 35 1 5 0 0 0 | 77. | 2 3751 0 39.8 31 2 5 0 0 0 | 78. | 3 3200 0 38.89 33 3 5 0 0 0 | 79. | 4 3673 0 39.61145 24.598 4 5 0 1 1 | 80. | 5 2581.58 . 38.97 35 5 5 1 0 0 | |----------------------------------------------------------------------------------------| 81. | 6 3001 0 41.02 38 6 5 0 0 0 | 82. | 7 1203 1 35.71356 51.1944 7 5 0 1 1 | 83. | 8 3652 0 42.04614 37.6994 8 5 0 1 1 | 84. | 9 3279 0 39.35 30 9 5 0 0 0 | 85. | 10 3007 0 39.53621 32.1937 10 5 0 1 1 | |----------------------------------------------------------------------------------------| 86. | 11 2887 0 38.9 28 11 5 0 0 0 | 87. | 12 3228.02 . 40.03 27 12 5 1 0 0 | 88. | 13 3375 0 41.59284 36 13 5 0 1 0 | 89. | 14 2002 1 36.48 37 14 5 0 0 0 | 90. | 15 2213 1 37.68 39 15 5 0 0 0 | +----------------------------------------------------------------------------------------+

In this file, the original data are shown on the first 15 lines, followed by 75 lines (5 x 15) with imputed values.

The ice command stored 5 sets of imputed data, as specified with the m(5) option. This generated missing value indicators, which begin with “nm” (abbrevation for “nonmissing”, but you can use anything you like) as we specified in the genmiss(nm) option. Notice that no imputation occurred for the variable lowbw, which was left out of the ice command. The imputed values are inserted in the original variable names in this file, but not in the data we have in Stata memory.

You can spot the imputed values, because they have more decimal places.


Whereas van Buuren describes this “regression switching” as,

“1. Specify the posterior predictive density p(Ymis|X,R), where X is a set of predictor variables, given the non-response mechanism p(R|Y,Z) and the complete data model p(Y,Z).”

Royston (2004, p. 232) explains this regression switching as,

“The algorithm is a type of Gibbs sampler in which the distribution of missing values of a covariate is sampled conditional on the distribution of the remaining covariates. Each variable in mainvarlist becomes in turn the response variable.”

This format is suitable for the micombine command, which will be used next.

The syntax for the micombine command is:

micombine regression_cmd [yvar][covarlist] [if][in][weight][, br detail eform(string) genxb(newvarname) impid(varname) lrr noconstant obsid(varname) svy[(svy_options)] regression_cmd_options]

where regression cmd includes clogit, cnreg, glm, logistic, logit, mlogit, nbreg, ologit, oprobit, poisson, probit, qreg, regress, rreg, stcox, streg, or xtgee. Other regression cmds will work but not all have been tested by the author. All weight types supported by regression cmd are allowed.

First, the data file created with the ice command must be loaded into memory, if they are not already there. The regression_cmd portion of the micombine is the same regression command we used before we imputed the data.

use bwtimp, clearmicombine regress bweight gestwks matage

Multiple imputation parameter estimates (5 imputations)------------------------------------------------------------------------------ bweight | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- gestwks | 324.7973 72.26509 4.49 0.001 167.3452 482.2494 matage | -64.41396 30.7788 -2.09 0.058 -131.4752 2.647278 _cons | -7567.114 2975.775 -2.54 0.026 -14050.77 -1083.457------------------------------------------------------------------------------15 observations.

This linear regression model represents the combined (a type of pooling) estimates from fitting the model to the five imputed datasets.


This model can be compared to the listwise deletion model we fitted above.

Listwise Deletion



Multiple Imputation

Multiple imputation parameter estimates (5 imputations)------------------------------------------------------------------------------ bweight | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- gestwks | 324.7973 72.26509 4.49 0.001 167.3452 482.2494 matage | -64.41396 30.7788 -2.09 0.058 -131.4752 2.647278 _cons | -7567.114 2975.775 -2.54 0.026 -14050.77 -1083.457------------------------------------------------------------------------------15 observations.

The large discrepancies are reflecting the differences that can exist in small sample sizes, where a single value can change model dramatically.


For a more fair comparison, we will use the original large dataset and try it again.

use births_with_missing, clearregress bweight gestwks matageice bweight gestwks matage , m(5) genmiss(nm) /// saving(bwtimp, replace) seed(888)use bwtimp, clearmicombine regress bweight gestwks matage

Listwise Deletion

Source | SS df MS Number of obs = 425-------------+------------------------------ F( 2, 422) = 206.17 Model | 79309893.1 2 39654946.6 Prob > F = 0.0000 Residual | 81166170.7 422 192336.898 R-squared = 0.4942-------------+------------------------------ Adj R-squared = 0.4918 Total | 160476064 424 378481.283 Root MSE = 438.56

------------------------------------------------------------------------------ bweight | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- gestwks | 201.6962 9.945484 20.28 0.000 182.1473 221.245 matage | .5083184 5.513141 0.09 0.927 -10.32832 11.34496 _cons | -4692.07 422.0691 -11.12 0.000 -5521.689 -3862.45------------------------------------------------------------------------------

Multiple Imputation

Multiple imputation parameter estimates (5 imputations)------------------------------------------------------------------------------ bweight | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- gestwks | 208.7919 9.449999 22.09 0.000 190.2251 227.3588 matage | .1029839 5.825347 0.02 0.986 -11.34236 11.54833 _cons | -4964.06 402.0698 -12.35 0.000 -5754.026 -4174.094------------------------------------------------------------------------------500 observations (imputation 1).

We see the models are much closer. In this case, we had 75 observations (15%) missing in the first model.


Just for fun, let’s compare these models to median and mean imputed models.

* -- median imputed modeluse births_with_missing, clear*capture drop nmbweightgen nmbweight=bweightcentile bweight, centile(50)replace nmbweight=r(c_1) if nmbweight==. // r(c_1) found using "return list"*capture drop nmgestwksgen nmgestwks=gestwkscentile gestwks, centile(50)replace nmgestwks=r(c_1) if nmgestwks==.*capture drop nmmatagegen nmmatage=matagecentile matage, centile(50)replace nmmatage=r(c_1) if nmmatage==.*regress nmbweight nmgestwks nmmatage

* -- mean imputed modeluse births_with_missing, clear*capture drop nmbweightgen nmbweight=bweightsum bweightreplace nmbweight=r(mean) if nmbweight==. *capture drop nmgestwksgen nmgestwks=gestwkssum gestwksreplace nmgestwks=r(mean) if nmgestwks==.*capture drop nmmatagegen nmmatage=matagesum matagereplace nmmatage=r(mean) if nmmatage==.*regress nmbweight nmgestwks nmmatage


1) Listwise deletion model

Source | SS df MS Number of obs = 425-------------+------------------------------ F( 2, 422) = 206.17 Model | 79309893.1 2 39654946.6 Prob > F = 0.0000 Residual | 81166170.7 422 192336.898 R-squared = 0.4942-------------+------------------------------ Adj R-squared = 0.4918 Total | 160476064 424 378481.283 Root MSE = 438.56

------------------------------------------------------------------------------ bweight | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- gestwks | 201.6962 9.945484 20.28 0.000 182.1473 221.245 matage | .5083184 5.513141 0.09 0.927 -10.32832 11.34496 _cons | -4692.07 422.0691 -11.12 0.000 -5521.689 -3862.45------------------------------------------------------------------------------

2) Multiple imputation model

Multiple imputation parameter estimates (5 imputations)------------------------------------------------------------------------------ bweight | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- gestwks | 208.7919 9.449999 22.09 0.000 190.2251 227.3588 matage | .1029839 5.825347 0.02 0.986 -11.34236 11.54833 _cons | -4964.06 402.0698 -12.35 0.000 -5754.026 -4174.094------------------------------------------------------------------------------500 observations (imputation 1).

3) Median imputed model

Source | SS df MS Number of obs = 500-------------+------------------------------ F( 2, 497) = 153.67 Model | 74160695.6 2 37080347.8 Prob > F = 0.0000 Residual | 119927799 497 241303.418 R-squared = 0.3821-------------+------------------------------ Adj R-squared = 0.3796 Total | 194088495 499 388954.899 Root MSE = 491.23

------------------------------------------------------------------------------ nmbweight | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- nmgestwks | 190.0368 10.8495 17.52 0.000 168.7203 211.3534 nmmatage | .2067422 5.721325 0.04 0.971 -11.03422 11.44771 _cons | -4247.992 457.7167 -9.28 0.000 -5147.29 -3348.694------------------------------------------------------------------------------

4) Mean imputed model

Source | SS df MS Number of obs = 500-------------+------------------------------ F( 2, 497) = 158.56 Model | 75577258.4 2 37788629.2 Prob > F = 0.0000 Residual | 118447042 497 238324.028 R-squared = 0.3895-------------+------------------------------ Adj R-squared = 0.3871 Total | 194024300 499 388826.253 Root MSE = 488.18

------------------------------------------------------------------------------ nmbweight | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- nmgestwks | 192.1832 10.80209 17.79 0.000 170.9599 213.4066 nmmatage | .2557455 5.68614 0.04 0.964 -10.91609 11.42758 _cons | -4327.432 454.9994 -9.51 0.000 -5221.391 -3433.473


------------------------------------------------------------------------------They are all pretty close to each other.


Version 11: Multiple Imputation









First, we declare the data to be mi (multiple imputation) data, requesting the marginal long style (mlong) because it is the most memory-efficient of the available styles.

mi set mlong

Second, we register our variables, using “imputed” if to be imputed.

mi register imputed bweight gestwks matage

Third, we impute the missing values for bweight, using the linear regression approach (like Stata’s impute command), where the missing value is predicted by gestwks and matage. We set the random number seed so we can duplicate our work and asked for 5 imputations.

mi impute regress bweight gestwks matage, rseed(888) add(5)

note: variables gestwks matage registered as imputed and used to model variable bweight; this may cause some observations to be omitted from the estimation and may lead to missing imputed values

Univariate imputation Imputations = 5Linear regression added = 5Imputed: m=1 through m=5 updated = 0

| Observations per m |---------------------------------------------- Variable | complete incomplete imputed | total---------------+-----------------------------------+---------- bweight | 13 2 2 | 15--------------------------------------------------------------(complete + incomplete = total; imputed is the minimum across m of the number of filled in observations.)

Note: right-hand-side variables (or weights) have missing values; model parameters estimated using listwise deletion

We were able to fill in the two missing values for bweight.

Fourth, we impute the missing values for gestwks, using the linear regression approach predicting from matage.

mi impute regress gestwks matage, rseed(999) add(5)

gestwks: missing imputed values produced This may occur when imputation variables are used as independent variables or when independent variables contain missing values. You can specify option force if you wish to proceed anyway.r(498);

The “force” option would keep from crashing, but nothing useful would come out of it. It appears we cannot impute gestwks due to missing values (no information) in matage.

Fifth, we impute the missing values for matage, using the linear regression approach predicting from gestwks


mi impute regress matage gestwks, rseed(999) add(5)

matage: missing imputed values produced This may occur when imputation variables are used as independent variables or when independent variables contain missing values. You can specify option force if you wish to proceed anyway.r(498);

The “force” option would keep from crashing, but nothing useful would come out of it. It appears we cannot impute matage due to missing values (no information) in gestwks.

Sixth, we check that the imputation did not create something crazy, but looking at the descriptive stats before imputation, after the first imputation, and at the fifth imputation.

mi xeq 0 1 5: sum bweight gestwks matage

m=0 data:-> sum bweight gestwks matage

Variable | Obs Mean Std. Dev. Min Max-------------+-------------------------------------------------------- bweight | 13 2912.538 741.7804 1203 3751 gestwks | 10 38.927 1.277533 36.48 41.02 matage | 11 33.54545 4.058661 27 39





We see the nonmissing sample size for matage increased, but nothing changed for the other two variables. It was a big change in the mean for bweight, which might make us wonder if the imputation worked well. We’ll see below it did not seem to cause a problem.


Finally, we run the linear regression model on the imputed variables. The dots options charts progress on the screen if it takes a long time.

mi estimate, dots: regress bweight gestwks matage

Imputations (5): ..... done

Multiple-imputation estimates Imputations = 5Linear regression Number of obs = 10 Average RVI = 0.2082 Complete DF = 7DF adjustment: Small sample DF: min = 5.01 avg = 5.33 max = 5.56Model F test: Equal FMI F( 2, 4.7) = 11.71Within VCE type: OLS Prob > F = 0.0146


Comparing this to the original model that used listwise deletion of missing values,



We see that the imputed modeled was based on n=2 more observations, which increased the statistical power slightly (smaller p value) for gestwks, while keeping the coefficient essentially the same.


Version 11: Multiple Imputation Using Imputaton Via Changed Equations (mi ice)

This approach will fill in more missing data than the preceding approach.

On the website, http://www.stata.com/support/faqs/stat/mi_ice.html, the way to get the original ice, which fills in more missing data, is described,

“In Stata 11, you can use the user-written command mi ice to perform imputation via chained equations. mi ice is available from Patrick Royston’s web page (net from http://www.homepages.ucl.ac.uk/~ucakjpr/stata/) under the heading mi_ice. mi ice is a wrapper for ice that understands the official mi data format.”

To add this to Stata-11, use

net from http://www.homepages.ucl.ac.uk/~ucakjpr/stata/

and then click on,

mi_ice Stata 11 version of -ice-; knows about the new MI format

-------------------------------------------------------------------------------package mi_ice from http://www.homepages.ucl.ac.uk/~ucakjpr/stata-------------------------------------------------------------------------------

TITLE mi ice. Stata 11-aware wrapper for the -ice- package

DESCRIPTION/AUTHOR(S) Program by Yulia Marchenko and Patrick Royston Distribution-Date: 20101130 version: 1.0.2 Note: for this Stata 11 program to work, you must first install -ice-. Please direct queries to Patrick Royston ([email protected])

INSTALLATION FILES (click here to install) mi_ice\mi_cmd_ice.ado mi_ice\mi_ice.sthlp-------------------------------------------------------------------------------(click here to return to the previous screen)

Clicking on the “(click here to install)” link loads the software into Stata.



mi set mlong



Third, we impute the missing values for bweight, gestwks, and matage using the method of chain equations. We set the random number seed so we can duplicate our work and asked for 5 imputations.

mi ice bweight gestwks matage , add(5) seed(888)

#missing | values | Freq. Percent Cum.------------+----------------------------------- 0 | 8 53.33 53.33 1 | 3 20.00 73.33 2 | 4 26.67 100.00------------+----------------------------------- Total | 15 100.00

Variable | Command | Prediction equation------------+---------+------------------------------------------------ bweight | regress | gestwks matage gestwks | regress | bweight matage matage | regress | bweight gestwks-----------------------------------------------------------------------Imputing 1..2..3..4..5..file C:\DOCUME~1\U00327~1.SRV\LOCALS~1\Temp\ST_0000006s.tmp saved(5 imputations added; M=5)


Fourth, we check that the imputation did not create something crazy, but looking at the descriptive stats before imputation, after the first imputation, and at the fifth imputation.







Variable | Obs Mean Std. Dev. Min Max-------------+-------------------------------------------------------- bweight | 15 2911.507 697.542 1203 3751 gestwks | 15 39.18468 1.725737 35.71356 42.04614 matage | 15 34.31236 6.361323 24.59798 51.19441

We don’t see anything strange. We also notice that the three variables are now all nonmissing.


Finally, we run the linear regression model on the imputed variables. The dots options charts progress on the screen if it takes a long time.


Imputations (5): ..... done

Multiple-imputation estimates Imputations = 5Linear regression Number of obs = 15 Average RVI = 1.2052 Complete DF = 12DF adjustment: Small sample DF: min = 2.62 avg = 4.98 max = 6.74Model F test: Equal FMI F( 2, 3.9) = 13.13Within VCE type: OLS Prob > F = 0.0186

------------------------------------------------------------------------------ bweight | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- gestwks | 324.7973 72.26509 4.49 0.005 144.5517 505.0429 matage | -64.41396 30.7788 -2.09 0.140 -170.8037 41.97578 _cons | -7567.114 2975.775 -2.54 0.040 -14658.97 -475.2537------------------------------------------------------------------------------

Comparing this to the original model that used listwise deletion of missing values,



We see that the imputed modeled was based on n=15 observations, which is the actual sample size of our dataset.

Here are all of the commands that we just used,

mi set mlongmi register imputed bweight gestwks matagemi ice bweight gestwks matage , add(5) seed(888)mi xeq 0 1 5: sum bweight gestwks matagemi estimate, dots: regress bweight gestwks matage


Version 12: Multiple Imputation Using Imputaton Via Changed Equations (mi impute chained)

The method of imputation by chained equations was officially added to Stata in version 12.









To see what variables having missing values, we can use the nmissing command we installed above, along with the “describe short” to get a list of all the variable names,

dsnmissing

. dsid bweight lowbw gestwks matage

. nmissing

bweight 2lowbw 2gestwks 5matage 4

We see that we have some missing data on all variables, except our subject ID variable that will not be included in the model, anyway. We do not intend to use low birth weight, lowbw, in our model to predicto birthweight, so we can ignore that variable.


mi set mlong



Third, we impute the missing values for bweight, gestwks, and matage using the method of chain equations, requesting 10 imputed datasets with the add(10) option. The (regress) part of the command instructs Stata to use linear regression to predict the missing values from the other variables. The rseed, where you select any number you want as the random number generator seed, is a way to be able to reproduce the imputation,

mi impute chained (regress) bweight gestwks matage , add(10) rseed(888)

Conditional models: bweight: regress bweight matage gestwks matage: regress matage bweight gestwks gestwks: regress gestwks bweight matage

Performing chained iterations ...

Multivariate imputation Imputations = 10Chained equations added = 5Imputed: m=6 through m=10 updated = 0

Initialization: monotone Iterations = 50 burn-in = 10


bweight: linear regression gestwks: linear regression matage: linear regression

------------------------------------------------------------------ | Observations per m |---------------------------------------------- Variable | Complete Incomplete Imputed | Total-------------------+-----------------------------------+---------- bweight | 13 2 2 | 15 gestwks | 10 5 5 | 15 matage | 11 4 4 | 15------------------------------------------------------------------(complete + incomplete = total; imputed is the minimum across m of the number of filled-in observations.)

Fourth, we check that the imputation did not create something crazy, but looking at the descriptive stats before imputation, after the first imputation, and at the fifth imputation.





Variable | Obs Mean Std. Dev. Min Max-------------+-------------------------------------------------------- bweight | 15 2906.259 711.6166 1203 3751 gestwks | 15 38.85626 1.335499 35.94739 41.02 matage | 15 33.56222 5.995813 26.79644 49.17725



We don’t see anything strange. The imputed datasets have descriptive statistics very similar to the original non-imputed dataset. We also notice that the three variables are now all nonmissing as they should be.


Finally, we run the linear regression model on the imputed variables. The dots options charts progress on the screen, which is helpful if it takes a long time.


Imputations (10): .........10 done

Multiple-imputation estimates Imputations = 10Linear regression Number of obs = 15 Average RVI = 0.7878 Largest FMI = 0.4927 Complete DF = 12DF adjustment: Small sample DF: min = 5.37 avg = 5.71 max = 6.16Model F test: Equal FMI F( 2, 6.4) = 13.60Within VCE type: OLS Prob > F = 0.0049


Notice the model is now based on a sample size of n=15. Comparing this to the original model that used listwise deletion of missing values, with a sample size of n=8 due to listwise deletion of missing data,



Here are all of the commands that we just used, so you have them in one place,

mi set mlongmi register imputed bweight gestwks matagemi impute chained (regress) bweight gestwks matage , add(10) rseed(888) mi xeq 0 1 5: sum bweight gestwks matagemi estimate, dots: regress bweight gestwks matage


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