# FIML in Lavaan: Descriptive Statistics

A new article created using the Distill format.

William Murrah www.statistical-thinking.com (QMER)aub.ie/qmer
Nov. 14, 2018

# FIML for Missing Data in Lavaan

Full information maximum likelihood (FIML) is a modern statistical technique for handling missing data. If you are not familiar with FIML, I would recommend the book entitled Applied Missing Data Analysis by Craig Enders. The book is both thorough and accessible, and a good place to start for those not familiar with the ins and outs of modern missing data techniques.

The purpose of the FIML in Lavaan series of posts and the related git repository is to take some of the examples related to FIML estimation within a regression framework from the Applied Missing Data website, and translate them into code for the R package lavaan. The code on the Applied Missing Data website in mostly for Mplus, which is quite expensive software. I hope this will give those who don’t have access to Mplus the ability to work through the examples using free and open source software.

In this first tutorial I start with the basics: how to get descriptive statistics using FIML. The data and Mplus code for this example can be found on the Book Examples page of the Applied Missing Data website. I also created a github repository with the data and R files with equivalent code in lavaan, which can be found here. Remember to replace the file path in the R code below with the file path to the folder in which you unzip the data files.

You will also want to read over the lavaan documentation and visit the very helpful lavaan website to take advantage of the tutorials there. With these resources at your disposal, you should be able to use replicate the examples in lavaan. Here, I walk through the major sections of the R code. This is the same code found in the github repository in the R file entitled FIMLdescriptivesCorrelations.R.

I always include a header with basic information in my code files.

#***********************************************************************
# section 4.14 Summary Statistics --------------------------------------
# Author: William M. Murrah
# Description: This code replicates the section 4.14 example on the
#              the appliedmissingdata.com website, which generates
#              descriptive statistics and correlations,
# Version history ------------------------------------------------------
# 2014.05.30: code created
#***********************************************************************
# R packages used
library(lavaan)


## Import and prepare data

First, import the data into R. MPlus uses .dat files which can only contain numbers. Variable names are not included in the .dat file, but instead are included in the Mplus .inp file. I use the read.table function to read the .dat file.

    employee <- read.table("data/employee.dat")


Next, I assign names to the variables in the new data frame.

    # Assign names to variables.
names(employee) <- c("id", "age", "tenure", "female", "wbeing",
"jobsat", "jobperf", "turnover", "iq")


The final step in preparing the data is to recode the data values -99, which are used as missing data values in the .dat file, to NA, which is the missing value indicator in R.

    # Replace all missing values (-99) with R missing value character 'NA'.
employee[employee==-99] <- NA


## Create Model Object

Now that the data are ready, I create a character string with the model using the lavaan syntax. For descriptives and correlations I model the mean, variances, and covariance/correlations.

    # Create descriptive model object
model <- '
# means
age      ~ 1
tenure   ~ 1
female   ~ 1
wbeing   ~ 1
jobsat   ~ 1
jobperf  ~ 1
turnover ~ 1
iq       ~ 1

# variances
age      ~~ age
tenure   ~~ tenure
female   ~~ female
wbeing   ~~ wbeing
jobsat   ~~ jobsat
jobperf  ~~ jobperf
turnover ~~ turnover
iq       ~~ iq

# covariances/correlations
age      ~~ tenure + female + wbeing + jobsat + jobperf + turnover + iq
tenure   ~~ female + wbeing + jobsat + jobperf + turnover + iq
female   ~~ wbeing + jobsat + jobperf + turnover + iq
wbeing   ~~ jobsat + jobperf + turnover + iq
jobsat   ~~ jobperf + turnover + iq
jobperf  ~~ turnover + iq
turnover ~~ iq
'


## Fit the Model

To fit the model, I use the lavaan sem function. This function takes the first two argument model and data. The third argument is missing ='fiml', which tells lavaan to use FIML (the default is to use listwise deletion).

    fit <- sem(model, employee, missing='fiml')


Alternatively, you could leave the section of the model code under the # means section and use the meanstructure=TRUE argument in the fit function as follows, which give the same results:

    fit <- sem(model, employee, missing='fiml', meanstructure=TRUE)


## Generate Output

To print the results to the console, use the summary function.

    summary(fit, fit.measures=TRUE, standardize=TRUE)


The fit.measures=TRUE calls fit statistics in the output. This should look familiar to those who have used Mplus.

lavaan (0.5-16) converged normally after 141 iterations

Number of observations                           480

Number of missing patterns                         3

Estimator                                         ML
Minimum Function Test Statistic                0.000
Degrees of freedom                                 0
P-value (Chi-square)                           1.000

Model test baseline model:

Minimum Function Test Statistic              527.884
Degrees of freedom                                28
P-value                                        0.000

User model versus baseline model:

Comparative Fit Index (CFI)                    1.000
Tucker-Lewis Index (TLI)                       1.000

Loglikelihood and Information Criteria:

Loglikelihood user model (H0)              -6621.805
Loglikelihood unrestricted model (H1)      -6621.805

Number of free parameters                         44
Akaike (AIC)                               13331.609
Bayesian (BIC)                             13515.256

Root Mean Square Error of Approximation:

RMSEA                                          0.000
90 Percent Confidence Interval          0.000  0.000
P-value RMSEA <= 0.05                          1.000

Standardized Root Mean Square Residual:

SRMR                                           0.000

The standardize=TRUE argument includes columns with standardized output. the std.all column in lavaan output is the same as the STDYX section in Mplus.

Parameter estimates:

Information                                 Observed
Standard Errors                             Standard

Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all
Covariances:
age ~~
tenure            8.459    0.858    9.865    0.000    8.459    0.504
female           -0.028    0.122   -0.229    0.819   -0.028   -0.010
wbeing            1.148    0.334    3.433    0.001    1.148    0.182
jobsat            0.861    0.340    2.531    0.011    0.861    0.136
jobperf          -0.330    0.308   -1.072    0.284   -0.330   -0.049
turnover         -0.377    0.116   -3.255    0.001   -0.377   -0.150
iq                0.674    2.066    0.326    0.744    0.674    0.015
tenure ~~
female           -0.052    0.071   -0.736    0.462   -0.052   -0.034
wbeing            0.569    0.195    2.916    0.004    0.569    0.155
jobsat            0.565    0.200    2.822    0.005    0.565    0.154
jobperf           0.061    0.178    0.344    0.731    0.061    0.016
turnover          0.016    0.066    0.240    0.810    0.016    0.011
iq                0.026    1.199    0.022    0.983    0.026    0.001
female ~~
wbeing            0.067    0.031    2.156    0.031    0.067    0.115
jobsat            0.028    0.031    0.881    0.378    0.028    0.047
jobperf          -0.009    0.029   -0.323    0.747   -0.009   -0.015
turnover          0.001    0.011    0.114    0.909    0.001    0.005
iq                0.284    0.192    1.481    0.139    0.284    0.068
wbeing ~~
jobsat            0.446    0.095    4.714    0.000    0.446    0.322
jobperf           0.671    0.084    8.030    0.000    0.671    0.456
turnover         -0.141    0.030   -4.768    0.000   -0.141   -0.257
iq                2.876    0.530    5.430    0.000    2.876    0.291
jobsat ~~
jobperf           0.271    0.080    3.378    0.001    0.271    0.184
turnover         -0.129    0.030   -4.248    0.000   -0.129   -0.234
iq                4.074    0.566    7.195    0.000    4.074    0.411
jobperf ~~
turnover         -0.203    0.028   -7.168    0.000   -0.203   -0.346
iq                4.496    0.523    8.588    0.000    4.496    0.426
turnover ~~
iq               -0.706    0.182   -3.872    0.000   -0.706   -0.180

Intercepts:
age              37.948    0.245  154.633    0.000   37.948    7.058
tenure           10.054    0.142   70.601    0.000   10.054    3.222
female            0.542    0.023   23.817    0.000    0.542    1.087
wbeing            6.288    0.062  100.701    0.000    6.288    5.349
jobsat            5.950    0.063   94.052    0.000    5.950    5.053
jobperf           6.021    0.057  105.262    0.000    6.021    4.805
turnover          0.321    0.021   15.058    0.000    0.321    0.687
iq              100.102    0.384  260.475    0.000  100.102   11.889

Variances:
age              28.908    1.866                     28.908    1.000
tenure            9.735    0.628                      9.735    1.000
female            0.248    0.016                      0.248    1.000
wbeing            1.382    0.107                      1.382    1.000
jobsat            1.386    0.108                      1.386    1.000
jobperf           1.570    0.101                      1.570    1.000
turnover          0.218    0.014                      0.218    1.000
iq               70.892    4.576                     70.892    1.000

Recall that correlations are standardized covariances, so correlations are found in the std.all column in the Covariances section. Also, intercepts are means, and can be interpreted as the FIML means for the variables.

Finally, to get the missing data patterns and covariance coverage output that can be included in Mplus output use the following code:

    # Get missing data patterns and covariance coverage similar
# to that found in Mplus output.
inspect(fit, 'patterns')
inspect(fit, 'coverage')


which leads to the following output:

### Missing Data Patterns

    age tenure female wbeing jobsat jobprf turnvr iq
160   1      1      1      1      1      1      1  1
160   1      1      1      1      0      1      1  1
160   1      1      1      0      1      1      1  1

### Covariance Coverage


age   tenure female wbeing jobsat jobprf turnvr iq
age      1.000
tenure   1.000 1.000
female   1.000 1.000  1.000
wbeing   0.667 0.667  0.667  0.667
jobsat   0.667 0.667  0.667  0.333  0.667
jobperf  1.000 1.000  1.000  0.667  0.667  1.000
turnover 1.000 1.000  1.000  0.667  0.667  1.000  1.000
iq       1.000 1.000  1.000  0.667  0.667  1.000  1.000  1.000