Mplus version 8 was used for these examples. All the files for this portion of this seminar can be downloaded here.
1.0 Descriptive statistics
To get basic descriptive statistics (means, variances,
covariances and correlations) in Mplus, a Type = basic; statement must be included in the
analysis command block. To view histograms or
scatterplots of some of the variables, a plot command
block should be included. These types of univariate and bivariate graphs are plot1
types of graphs.
The data set used in the following example is hsb.dat .
title: Exploring data
data:
file is hsb.dat;
variable:
names are
id female race ses schtyp prog read write math science socst;
usevariables are
id female race ses schtyp prog read write math science socst;
analysis:
type = basic;
plot:
type is plot1;
Here is the output that Mplus generates.
INPUT READING TERMINATED NORMALLY
Entering data example free format using hsb.dat
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 200
Number of dependent variables 11
Number of independent variables 0
Number of continuous latent variables 0
Observed dependent variables
Continuous
ID FEMALE RACE SES SCHTYP PROG
READ WRITE MATH SCIENCE SOCST
Estimator ML
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Input data file(s)
hsb.dat
Input data format FREE
RESULTS FOR BASIC ANALYSIS
SAMPLE STATISTICS
Means
ID FEMALE RACE SES SCHTYP
________ ________ ________ ________ ________
1 100.500 0.545 3.430 2.055 1.160
Means
PROG READ WRITE MATH SCIENCE
________ ________ ________ ________ ________
1 2.025 52.230 52.775 52.645 51.850
Means
SOCST
________
1 52.405
Covariances
ID FEMALE RACE SES SCHTYP
________ ________ ________ ________ ________
ID 3333.250
FEMALE -2.508 0.248
RACE 44.825 0.001 1.075
SES 8.797 -0.045 0.146 0.522
SCHTYP 10.210 0.003 0.041 0.036 0.134
PROG -2.308 0.001 -0.036 0.009 -0.024
READ 87.755 -0.270 2.581 2.167 0.323
WRITE 101.907 1.208 2.157 1.417 0.441
MATH 118.282 -0.137 1.963 1.840 0.337
SCIENCE 183.260 -0.628 3.280 2.018 0.234
SOCST 113.332 0.279 2.111 2.568 0.380
Covariances
PROG READ WRITE MATH SCIENCE
________ ________ ________ ________ ________
PROG 0.474
READ -0.951 104.597
WRITE -1.179 57.707 89.394
MATH -0.966 63.297 54.555 87.329
SCIENCE -1.291 63.650 53.266 58.212 97.537
SOCST -1.440 68.067 61.236 54.489 49.191
Covariances
SOCST
________
SOCST 114.681
Correlations
ID FEMALE RACE SES SCHTYP
________ ________ ________ ________ ________
ID 1.000
FEMALE -0.087 1.000
RACE 0.749 0.001 1.000
SES 0.211 -0.125 0.195 1.000
SCHTYP 0.482 0.015 0.108 0.137 1.000
PROG -0.058 0.004 -0.050 0.017 -0.095
READ 0.149 -0.053 0.243 0.293 0.086
WRITE 0.187 0.256 0.220 0.207 0.127
MATH 0.219 -0.029 0.203 0.272 0.098
SCIENCE 0.321 -0.128 0.320 0.283 0.065
SOCST 0.183 0.052 0.190 0.332 0.097
Correlations
PROG READ WRITE MATH SCIENCE
________ ________ ________ ________ ________
PROG 1.000
READ -0.135 1.000
WRITE -0.181 0.597 1.000
MATH -0.150 0.662 0.617 1.000
SCIENCE -0.190 0.630 0.570 0.631 1.000
SOCST -0.195 0.621 0.605 0.544 0.465
Correlations
SOCST
________
SOCST 1.000
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
ID 100.500 0.000 1.000 0.50% 40.000 80.000 100.500
200.000 3333.250 -1.200 200.000 0.50% 120.000 160.000
FEMALE 0.545 -0.181 0.000 45.50% 0.000 0.000 1.000
200.000 0.248 -1.967 1.000 54.50% 1.000 1.000
RACE 3.430 -1.576 1.000 12.00% 3.000 4.000 4.000
200.000 1.075 0.888 4.000 72.50% 4.000 4.000
SES 2.055 -0.083 1.000 23.50% 1.000 2.000 2.000
200.000 0.522 -1.083 3.000 29.00% 2.000 3.000
SCHTYP 1.160 1.855 1.000 84.00% 1.000 1.000 1.000
200.000 0.134 1.440 2.000 16.00% 1.000 1.000
PROG 2.025 -0.032 1.000 22.50% 1.000 2.000 2.000
200.000 0.474 -0.892 3.000 25.00% 2.000 3.000
READ 52.230 0.195 28.000 0.50% 44.000 47.000 50.000
200.000 104.597 -0.637 76.000 1.00% 55.000 63.000
WRITE 52.775 -0.478 31.000 2.00% 44.000 52.000 54.000
200.000 89.394 -0.761 67.000 3.50% 57.000 62.000
MATH 52.645 0.284 33.000 0.50% 43.000 49.000 52.000
200.000 87.329 -0.663 75.000 1.00% 55.000 61.000
SCIENCE 51.850 -0.187 26.000 0.50% 42.000 50.000 53.000
200.000 97.537 -0.572 74.000 0.50% 55.000 61.000
SOCST 52.405 -0.379 26.000 1.50% 41.000 51.000 52.000
200.000 114.681 -0.541 71.000 4.00% 56.000 61.000
PLOT INFORMATION
The following plots are available:
Histograms (sample values)
Scatterplots (sample values)
DIAGRAM INFORMATION
Mplus diagrams are currently not available for TYPE=BASIC.
No diagram output was produced.
You can compare these summary statistics to those found in another software package or by hand to
ensure that you have read the data into Mplus correctly.
To view plots, you can select Plots -> View plots or press Alt-V to open
the dialog box below.
From here, you can select Histograms and choose read from the drop down menu
to get the plot below.
Alternatively, you can select Scatterplots and choose to look at math
and write.
2.0 Descriptive statistics with missing data without listwise deletion
Next, we will look at a dataset with missing data. This time we will not
include the id variable in the analyses. We will use the hsbmis.dat datafile and hsbmis.inp
command file created by Stata in the previous section to demonstrate the descriptive statistics.
title: Exploratory analysis with missing data
data:
file is hsbmis.dat
variable:
names are
id female race ses schtyp prog read write math science socst;
missing are all (-9999);
usevariables are
female race ses schtyp prog read write math science socst;
analysis:
type = basic;
Here is the output generated by Mplus.
INPUT READING TERMINATED NORMALLY
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 200
Number of dependent variables 10
Number of independent variables 0
Number of continuous latent variables 0
Observed dependent variables
Continuous
FEMALE RACE SES SCHTYP PROG READ
WRITE MATH SCIENCE SOCST
Estimator ML
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Input data file(s)
hsbmis.dat
Input data format FREE
SUMMARY OF DATA
Number of missing data patterns 7
SUMMARY OF MISSING DATA PATTERNS
MISSING DATA PATTERNS (x = not missing)
1 2 3 4 5 6 7
FEMALE x x x x x x
RACE x x x x x x x
SES x x x x x x x
SCHTYP x x x x x x x
PROG x x x x x x x
READ x x x x x x
WRITE x x x x x x
MATH x x x x x x
SCIENCE x x x x x x
SOCST x x x x x x
MISSING DATA PATTERN FREQUENCIES
Pattern Frequency Pattern Frequency Pattern Frequency
1 138 4 12 7 6
2 5 5 14
3 14 6 11
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
FEMALE RACE SES SCHTYP PROG
________ ________ ________ ________ ________
FEMALE 0.970
RACE 0.970 1.000
SES 0.970 1.000 1.000
SCHTYP 0.970 1.000 1.000 1.000
PROG 0.970 1.000 1.000 1.000 1.000
READ 0.915 0.945 0.945 0.945 0.945
WRITE 0.900 0.930 0.930 0.930 0.930
MATH 0.910 0.940 0.940 0.940 0.940
SCIENCE 0.900 0.930 0.930 0.930 0.930
SOCST 0.945 0.975 0.975 0.975 0.975
Covariance Coverage
READ WRITE MATH SCIENCE SOCST
________ ________ ________ ________ ________
READ 0.945
WRITE 0.875 0.930
MATH 0.885 0.870 0.940
SCIENCE 0.875 0.860 0.870 0.930
SOCST 0.920 0.905 0.915 0.905 0.975
RESULTS FOR BASIC ANALYSIS
ESTIMATED SAMPLE STATISTICS
Means
FEMALE RACE SES SCHTYP PROG
________ ________ ________ ________ ________
1 0.546 3.430 2.055 1.160 2.025
Means
READ WRITE MATH SCIENCE SOCST
________ ________ ________ ________ ________
1 52.326 52.561 52.768 51.852 52.354
Covariances
FEMALE RACE SES SCHTYP PROG
________ ________ ________ ________ ________
FEMALE 0.247
RACE 0.015 1.075
SES -0.041 0.146 0.522
SCHTYP 0.003 0.041 0.036 0.134
PROG 0.008 -0.036 0.009 -0.024 0.474
READ -0.259 2.626 2.281 0.364 -0.959
WRITE 1.193 2.053 1.388 0.475 -1.202
MATH -0.253 2.076 1.658 0.237 -1.117
SCIENCE -0.596 3.066 1.859 0.295 -1.461
SOCST 0.256 2.042 2.548 0.388 -1.435
Covariances
READ WRITE MATH SCIENCE SOCST
________ ________ ________ ________ ________
READ 104.556
WRITE 56.806 88.288
MATH 61.093 53.278 84.485
SCIENCE 64.333 54.832 58.322 94.201
SOCST 67.681 60.178 50.695 50.635 115.474
Correlations
FEMALE RACE SES SCHTYP PROG
________ ________ ________ ________ ________
FEMALE 1.000
RACE 0.029 1.000
SES -0.113 0.195 1.000
SCHTYP 0.014 0.108 0.137 1.000
PROG 0.024 -0.050 0.017 -0.095 1.000
READ -0.051 0.248 0.309 0.097 -0.136
WRITE 0.255 0.211 0.204 0.138 -0.186
MATH -0.055 0.218 0.250 0.070 -0.176
SCIENCE -0.123 0.305 0.265 0.083 -0.219
SOCST 0.048 0.183 0.328 0.099 -0.194
Correlations
READ WRITE MATH SCIENCE SOCST
________ ________ ________ ________ ________
READ 1.000
WRITE 0.591 1.000
MATH 0.650 0.617 1.000
SCIENCE 0.648 0.601 0.654 1.000
SOCST 0.616 0.596 0.513 0.485 1.000
MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -4148.435
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
FEMALE 0.546 -0.186 0.000 45.36% 0.000 0.000 1.000
194.000 0.248 -1.965 1.000 54.64% 1.000 1.000
RACE 3.430 -1.576 1.000 12.00% 3.000 4.000 4.000
200.000 1.075 0.888 4.000 72.50% 4.000 4.000
SES 2.055 -0.083 1.000 23.50% 1.000 2.000 2.000
200.000 0.522 -1.083 3.000 29.00% 2.000 3.000
SCHTYP 1.160 1.855 1.000 84.00% 1.000 1.000 1.000
200.000 0.134 1.440 2.000 16.00% 1.000 1.000
PROG 2.025 -0.032 1.000 22.50% 1.000 2.000 2.000
200.000 0.474 -0.892 3.000 25.00% 2.000 3.000
READ 52.397 0.140 28.000 0.53% 44.000 48.000 52.000
189.000 105.160 -0.668 76.000 1.06% 55.000 63.000
WRITE 52.731 -0.482 31.000 2.15% 44.000 52.000 54.000
186.000 88.777 -0.766 67.000 3.23% 57.000 62.000
MATH 52.532 0.314 33.000 0.53% 43.000 49.000 52.000
188.000 84.334 -0.575 75.000 1.06% 55.000 61.000
SCIENCE 51.763 -0.231 26.000 0.54% 42.000 50.000 53.000
186.000 93.654 -0.527 74.000 0.54% 55.000 61.000
SOCST 52.441 -0.378 26.000 1.54% 41.000 51.000 52.000
195.000 115.518 -0.541 71.000 4.10% 56.000 61.000
DIAGRAM INFORMATION
Mplus diagrams are currently not available for TYPE=BASIC.
No diagram output was produced.
In the first section, “SUMMARY OF ANALYSIS”, we see that the “Number of Observations” used is 200, the total number of observations in the data set. Additionally, we see that the “Estimator” used is “ML”, which is short for Maximum Likelihood. By default Mplus uses the maximum likelihood estimation, and it uses all the available
values instead of doing deleting any observations with missing (listwise deletion). Because of this, the descriptive statistics from Mplus do not match
with the output from a standard statistics software package, such as SPSS, Stata, SAS, or R, which use listwise deletion when missing data are present.
In the section of the Mplus output titled “SUMMARY OF MISSING DATA PATTERNS”, we can see which combinations of variables are missing for how many observations in our data. From this section of output, we can see that we have 138 complete observations and no more than one missing variable in any of our other observations. There is a portion of the output labeled “COVARIANCE COVERAGE.” This matrix gives the proportion of values present for each variable individually (on the diagonal) and pairwise combinations of variables (below the diagonal).
3.0 Descriptive statistics with missing data with listwise deletion
For the purpose of comparing the results of descriptive statistics run
in SAS, Stata or SPSS against the results obtained from Mplus to ensure that your data
have been read into Mplus correctly, you can request that Mplus
does listwise deletion as well. Here is the syntax. Notice in “SUMMARY OF ANALYSIS” that only 138 observations are used with listwise deletion.l
title: Exploring data with listwise deletion of missing data
data:
file is hsbmis.dat;
listwise = on;
variable:
names are
id female race ses schtyp prog read write math science socst;
missing are all (-9999);
usevariables are
female race ses schtyp prog read write math science socst;
analysis:
type = basic;
INPUT READING TERMINATED NORMALLY
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 138
Number of dependent variables 10
Number of independent variables 0
Number of continuous latent variables 0
Observed dependent variables
Continuous
FEMALE RACE SES SCHTYP PROG READ
WRITE MATH SCIENCE SOCST
Estimator ML
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Input data file(s)
hsbmis.dat
Input data format FREE
RESULTS FOR BASIC ANALYSIS
SAMPLE STATISTICS
Means
FEMALE RACE SES SCHTYP PROG
________ ________ ________ ________ ________
1 0.565 3.442 2.058 1.167 2.043
Means
READ WRITE MATH SCIENCE SOCST
________ ________ ________ ________ ________
1 52.442 52.630 52.913 52.065 52.696
Covariances
FEMALE RACE SES SCHTYP PROG
________ ________ ________ ________ ________
FEMALE 0.246
RACE 0.018 1.102
SES -0.026 0.105 0.533
SCHTYP -0.007 0.057 0.019 0.139
PROG 0.004 -0.063 -0.024 -0.022 0.491
READ -0.054 2.739 1.634 0.151 -1.360
WRITE 1.165 1.656 1.275 0.417 -1.332
MATH -0.139 2.017 1.578 0.275 -1.228
SCIENCE -0.334 3.167 1.648 0.351 -1.764
SOCST 0.397 2.301 2.373 0.486 -1.951
Covariances
READ WRITE MATH SCIENCE SOCST
________ ________ ________ ________ ________
READ 99.305
WRITE 59.555 90.653
MATH 57.495 53.250 79.819
SCIENCE 63.102 56.379 56.622 95.742
SOCST 73.693 64.438 54.887 56.665 122.429
Correlations
FEMALE RACE SES SCHTYP PROG
________ ________ ________ ________ ________
FEMALE 1.000
RACE 0.035 1.000
SES -0.071 0.137 1.000
SCHTYP -0.039 0.145 0.071 1.000
PROG 0.013 -0.085 -0.047 -0.083 1.000
READ -0.011 0.262 0.225 0.041 -0.195
WRITE 0.247 0.166 0.183 0.117 -0.200
MATH -0.031 0.215 0.242 0.083 -0.196
SCIENCE -0.069 0.308 0.231 0.096 -0.257
SOCST 0.072 0.198 0.294 0.118 -0.252
Correlations
READ WRITE MATH SCIENCE SOCST
________ ________ ________ ________ ________
READ 1.000
WRITE 0.628 1.000
MATH 0.646 0.626 1.000
SCIENCE 0.647 0.605 0.648 1.000
SOCST 0.668 0.612 0.555 0.523 1.000
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
FEMALE 0.565 -0.263 0.000 43.48% 0.000 0.000 1.000
138.000 0.246 -1.931 1.000 56.52% 1.000 1.000
RACE 3.442 -1.595 1.000 12.32% 3.000 4.000 4.000
138.000 1.102 0.878 4.000 74.64% 4.000 4.000
SES 2.058 -0.090 1.000 23.91% 1.000 2.000 2.000
138.000 0.533 -1.121 3.000 29.71% 2.000 3.000
SCHTYP 1.167 1.789 1.000 83.33% 1.000 1.000 1.000
138.000 0.139 1.200 2.000 16.67% 1.000 1.000
PROG 2.043 -0.060 1.000 22.46% 1.000 2.000 2.000
138.000 0.491 -0.963 3.000 26.81% 2.000 3.000
READ 52.442 0.144 31.000 0.72% 44.000 50.000 52.000
138.000 99.305 -0.688 76.000 0.72% 55.000 63.000
WRITE 52.630 -0.465 31.000 2.17% 44.000 52.000 54.000
138.000 90.653 -0.781 67.000 4.35% 57.000 62.000
MATH 52.913 0.212 33.000 0.72% 45.000 50.000 53.000
138.000 79.819 -0.518 75.000 1.45% 56.000 61.000
SCIENCE 52.065 -0.271 26.000 0.72% 42.000 50.000 53.000
138.000 95.742 -0.459 74.000 0.72% 55.000 61.000
SOCST 52.696 -0.441 26.000 2.17% 44.000 51.000 54.000
138.000 122.429 -0.451 71.000 5.07% 56.000 61.000
DIAGRAM INFORMATION
Mplus diagrams are currently not available for TYPE=BASIC.
No diagram output was produced.