Examples

Descriptives

# Prints basic descriptive statistics
sem_descriptives(data)

Descriptive Statistics
Variable	n	Mean	SD	min	max	Skewness	Kurtosis
x1	75	5.05	0.73	3.78	6.74	0.26	-0.69
x2	75	4.79	1.51	1.39	7.87	-0.36	-0.50
x3	75	3.56	1.41	1.00	6.42	0.09	-0.88
y1	75	5.46	2.62	1.25	10.00	-0.10	-1.10
y2	75	4.26	3.95	0.00	10.00	0.33	-1.43
y3	75	6.56	3.28	0.00	10.00	-0.62	-0.66
y4	75	4.45	3.35	0.00	10.00	0.12	-1.16
y5	75	5.14	2.61	0.00	10.00	-0.24	-0.72
y6	75	2.98	3.37	0.00	10.00	0.93	-0.40
y7	75	6.20	3.29	0.00	10.00	-0.58	-0.67
y8	75	4.04	3.25	0.00	10.00	0.46	-0.91

Correlation Matrix

# Uses sjPlot to print a nice looking correlation table
sjt.corr(data, na.deletion = "pairwise", digits = 2)

	y1	y2	y3	y4	y5	y6	y7	y8	x1	x2	x3
y1		0.60***	0.68***	0.69***	0.74***	0.65***	0.67***	0.67***	0.38***	0.32**	0.25*
y2	0.60***		0.45***	0.72***	0.54***	0.71***	0.58***	0.61***	0.21	0.25*	0.21
y3	0.68***	0.45***		0.61***	0.58***	0.43***	0.65***	0.53***	0.33**	0.31**	0.23
y4	0.69***	0.72***	0.61***		0.65***	0.66***	0.68***	0.74***	0.47***	0.44***	0.39***
y5	0.74***	0.54***	0.58***	0.65***		0.56***	0.68***	0.63***	0.56***	0.52***	0.43***
y6	0.65***	0.71***	0.43***	0.66***	0.56***		0.61***	0.75***	0.34**	0.35**	0.33**
y7	0.67***	0.58***	0.65***	0.68***	0.68***	0.61***		0.71***	0.39***	0.40***	0.35**
y8	0.67***	0.61***	0.53***	0.74***	0.63***	0.75***	0.71***		0.46***	0.46***	0.37**
x1	0.38***	0.21	0.33**	0.47***	0.56***	0.34**	0.39***	0.46***		0.89***	0.80***
x2	0.32**	0.25*	0.31**	0.44***	0.52***	0.35**	0.40***	0.46***	0.89***		0.85***
x3	0.25*	0.21	0.23	0.39***	0.43***	0.33**	0.35**	0.37**	0.80***	0.85***
Computed correlation used pearson-method with pairwise-deletion.

CFA

# factors is a list of the latent factor names. To be used for printing lavaan output to nice looking tables. Not needed to run actual lavaan model
factors <- c("ind60", "dem60", "dem65")
# Specify the model parameters. Must be incased within single or double quotes. Can add labels to organize parameter specifications. I provided just some example labels, they are not required though and you can use whatever labels you want. You need to know how lavaan works! See http://lavaan.ugent.be/tutorial/index.html for more information on how to specify the model parameters
model <- '
# latent factors
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + y8

# correlated errors
y1 ~~ y5
y2 ~~ y4 + y6
y3 ~~ y7
y4 ~~ y8
y6 ~~ y8

# constraints

'
# You might want to specify other arguments. But this is pretty standard. 
#std.lv = TRUE means that the latent factor variances are set to 1. If False, then the path for the first variable on the factor specificed in the model will be set to 1.
fit <- cfa(model=model, data=data, mimic = mimic, missing=missing, std.lv = TRUE)

Summary Output

sem_sig(fit)

Model Significance
Sample.Size	Chi.Square	df	p.value
75	38.125	35	0.329

sem_fitmeasures(fit)

Model Fit Measures
CFI	RMSEA	RMSEA.Lower	RMSEA.Upper	AIC	BIC
0.995	0.035	0	0.092	3179.582	3276.916

sem_factorloadings(fit)

Factor Loadings
		Loadings
Latent Factor	Indicator	Standardized	Unstandardized	SE	z	sig
ind60	x1	0.920	0.670	0.065	10.339	***
ind60	x2	0.973	1.460	0.128	11.423	***
ind60	x3	0.872	1.218	0.128	9.489	***
dem60	y1	0.850	2.223	0.253	8.789	***
dem60	y2	0.717	2.794	0.408	6.850	***
dem60	y3	0.722	2.351	0.341	6.902	***
dem60	y4	0.846	2.812	0.324	8.677	***
dem65	y5	0.808	2.103	0.256	8.210	***
dem65	y6	0.746	2.493	0.341	7.320	***
dem65	y7	0.824	2.691	0.319	8.441	***
dem65	y8	0.828	2.662	0.316	8.430	***

sem_factorcor(fit, factors = factors)

Latent Factor Correlations
Factor 1	Factor 2	r	sig
ind60	dem60	0.447	***
ind60	dem65	0.578	***
dem60	dem65	0.967	***

sem_factorvar(fit, factors = factors)

Latent Factor Variance/Residual Variance
Factor 1	Factor 2	var	var.std	sig

sem_rsquared(fit)

R-Squared Values
Variable	R-Squared
x1	0.8461294
x2	0.9467924
x3	0.7606256
y1	0.7232242
y2	0.5142640
y3	0.5217883
y4	0.7152245
y5	0.6528920
y6	0.5565270
y7	0.6784378
y8	0.6853215

Diagram Output

semPaths(fit, whatLabels = "std", edge.label.cex = .5, layout = "tree2", rotation = 2, style = "lisrel", intercepts = FALSE, residuals = TRUE, curve = 1, curvature = 3, nCharNodes = 8, sizeMan = 6, sizeMan2 = 3, optimizeLatRes = TRUE, edge.color = "#000000", latents = factors)

Residual Correlation Matrix

sem_residuals(fit)

	x1	x2	x3	y1	y2	y3	y4	y5	y6	y7
x1
x2	0.00
x3	0.00	0.00
y1	0.03	-0.05	-0.08
y2	-0.08	-0.06	-0.07	-0.01
y3	0.03	0.00	-0.06	0.06	-0.07
y4	0.12	0.08	0.06	-0.03	0.01	0.00
y5	0.14	0.07	0.02	-0.02	-0.02	0.01	-0.01
y6	-0.05	-0.06	-0.04	0.04	0.02	-0.09	0.05	-0.04
y7	-0.05	-0.06	-0.06	0.00	0.01	0.00	0.01	0.01	-0.01
y8	0.02	-0.01	-0.05	-0.01	0.03	-0.05	0.03	-0.04	0.01	0.03

Full Output

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

## lavaan 0.6-3 ended normally after 75 iterations
## 
##   Optimization method                           NLMINB
##   Number of free parameters                         42
## 
##   Number of observations                            75
##   Number of missing patterns                         1
## 
##   Estimator                                         ML
##   Model Fit Test Statistic                      38.125
##   Degrees of freedom                                35
##   P-value (Chi-square)                           0.329
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic              730.654
##   Degrees of freedom                                55
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.995
##   Tucker-Lewis Index (TLI)                       0.993
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -1547.791
##   Loglikelihood unrestricted model (H1)      -1528.728
## 
##   Number of free parameters                         42
##   Akaike (AIC)                                3179.582
##   Bayesian (BIC)                              3276.916
##   Sample-size adjusted Bayesian (BIC)         3144.543
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.035
##   90 Percent Confidence Interval          0.000  0.092
##   P-value RMSEA <= 0.05                          0.611
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.041
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Observed information based on                Hessian
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   ind60 =~                                                              
##     x1                0.670    0.065   10.339    0.000    0.670    0.920
##     x2                1.460    0.128   11.423    0.000    1.460    0.973
##     x3                1.218    0.128    9.489    0.000    1.218    0.872
##   dem60 =~                                                              
##     y1                2.223    0.253    8.789    0.000    2.223    0.850
##     y2                2.794    0.408    6.850    0.000    2.794    0.717
##     y3                2.351    0.341    6.902    0.000    2.351    0.722
##     y4                2.812    0.324    8.677    0.000    2.812    0.846
##   dem65 =~                                                              
##     y5                2.103    0.256    8.210    0.000    2.103    0.808
##     y6                2.493    0.341    7.320    0.000    2.493    0.746
##     y7                2.691    0.319    8.441    0.000    2.691    0.824
##     y8                2.662    0.316    8.430    0.000    2.662    0.828
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .y1 ~~                                                                 
##    .y5                0.624    0.369    1.690    0.091    0.624    0.296
##  .y2 ~~                                                                 
##    .y4                1.313    0.699    1.879    0.060    1.313    0.273
##    .y6                2.153    0.726    2.964    0.003    2.153    0.356
##  .y3 ~~                                                                 
##    .y7                0.795    0.621    1.280    0.201    0.795    0.191
##  .y4 ~~                                                                 
##    .y8                0.348    0.458    0.761    0.447    0.348    0.109
##  .y6 ~~                                                                 
##    .y8                1.356    0.572    2.371    0.018    1.356    0.338
##   ind60 ~~                                                              
##     dem60             0.447    0.105    4.267    0.000    0.447    0.447
##     dem65             0.578    0.089    6.466    0.000    0.578    0.578
##   dem60 ~~                                                              
##     dem65             0.967    0.029   32.840    0.000    0.967    0.967
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .x1                5.054    0.084   60.127    0.000    5.054    6.943
##    .x2                4.792    0.173   27.657    0.000    4.792    3.194
##    .x3                3.558    0.161   22.066    0.000    3.558    2.548
##    .y1                5.465    0.302   18.104    0.000    5.465    2.090
##    .y2                4.256    0.450    9.461    0.000    4.256    1.093
##    .y3                6.563    0.376   17.460    0.000    6.563    2.016
##    .y4                4.453    0.384   11.598    0.000    4.453    1.339
##    .y5                5.136    0.301   17.092    0.000    5.136    1.974
##    .y6                2.978    0.386    7.717    0.000    2.978    0.891
##    .y7                6.196    0.377   16.427    0.000    6.196    1.897
##    .y8                4.043    0.371   10.889    0.000    4.043    1.257
##     ind60             0.000                               0.000    0.000
##     dem60             0.000                               0.000    0.000
##     dem65             0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .x1                0.082    0.020    4.136    0.000    0.082    0.154
##    .x2                0.120    0.070    1.712    0.087    0.120    0.053
##    .x3                0.467    0.089    5.233    0.000    0.467    0.239
##    .y1                1.891    0.469    4.035    0.000    1.891    0.277
##    .y2                7.373    1.346    5.479    0.000    7.373    0.486
##    .y3                5.067    0.968    5.233    0.000    5.067    0.478
##    .y4                3.148    0.756    4.165    0.000    3.148    0.285
##    .y5                2.351    0.489    4.810    0.000    2.351    0.347
##    .y6                4.954    0.895    5.532    0.000    4.954    0.443
##    .y7                3.431    0.728    4.715    0.000    3.431    0.322
##    .y8                3.254    0.707    4.603    0.000    3.254    0.315
##     ind60             1.000                               1.000    1.000
##     dem60             1.000                               1.000    1.000
##     dem65             1.000                               1.000    1.000

varTable(fit)

##    name idx nobs    type exo user  mean    var nlev lnam
## 1    x1   9   75 numeric   0    0 5.054  0.537    0     
## 2    x2  10   75 numeric   0    0 4.792  2.282    0     
## 3    x3  11   75 numeric   0    0 3.558  1.976    0     
## 4    y1   1   75 numeric   0    0 5.465  6.879    0     
## 5    y2   2   75 numeric   0    0 4.256 15.580    0     
## 6    y3   3   75 numeric   0    0 6.563 10.764    0     
## 7    y4   4   75 numeric   0    0 4.453 11.219    0     
## 8    y5   5   75 numeric   0    0 5.136  6.826    0     
## 9    y6   6   75 numeric   0    0 2.978 11.375    0     
## 10   y7   7   75 numeric   0    0 6.196 10.799    0     
## 11   y8   8   75 numeric   0    0 4.043 10.534    0

modificationIndices(fit, sort.=TRUE, minimum.value=3)

##      lhs op rhs    mi    epc sepc.lv sepc.all sepc.nox
## 52 ind60 =~  y4 4.796  0.577   0.577    0.174    0.174
## 53 ind60 =~  y5 4.456  0.559   0.559    0.215    0.215
## 70 dem65 =~  y4 4.260  2.986   2.986    0.898    0.898
## 99    y1 ~~  y3 3.771  0.849   0.849    0.274    0.274
## 74    x1 ~~  y2 3.040 -0.155  -0.155   -0.200   -0.200

SEM

# factors is a list of the latent factor names. To be used for printing lavaan output to nice looking tables. Not needed to run actual lavaan model
factors <- c("ind60", "dem60", "dem65")
# Specify the model parameters. Must be incased within single or double quotes. Can add labels to organize parameter specifications. I provided just some example labels, they are not required though and you can use whatever labels you want. You need to know how lavaan works! See http://lavaan.ugent.be/tutorial/index.html for more information on how to specify the model parameters
model <- '
# latent factors
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + y8

# correlated errors
y1 ~~ y5
y2 ~~ y4 + y6
y3 ~~ y7
y4 ~~ y8
y6 ~~ y8

# regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60

# latent covariances

# latent variances

'
# You might want to specify other arguments. But this is pretty standard. 
#std.lv = TRUE means that the latent factor variances are set to 1. If False, then the path for the first variable on the factor specificed in the model will be set to 1. For an SEM, it is better to set as FALSE. And if you want a latent factor variance set to 1 then specify it in the model and include NA* before the first variable on the factor. See http://lavaan.ugent.be/tutorial/index.html for more details
fit <- sem(model=model, data=data, mimic = "EQS", missing=missing, std.lv = FALSE)

Summary Output

sem_sig(fit)

Model Significance
Sample.Size	Chi.Square	df	p.value
75	37.617	35	0.35

sem_fitmeasures(fit)

Model Fit Measures
CFI	RMSEA	RMSEA.Lower	RMSEA.Upper	AIC	BIC
0.996	0.032	0	0.091	3179.582	3276.916

sem_factorloadings(fit)

Factor Loadings
		Loadings
Latent Factor	Indicator	Standardized	Unstandardized	SE	z	sig
ind60	x1	0.920	1.000	0.000
ind60	x2	0.973	2.180	0.140	15.580	***
ind60	x3	0.872	1.819	0.153	11.869	***
dem60	y1	0.850	1.000	0.000
dem60	y2	0.717	1.257	0.187	6.730	***
dem60	y3	0.722	1.058	0.149	7.083	***
dem60	y4	0.846	1.265	0.152	8.335	***
dem65	y5	0.808	1.000	0.000
dem65	y6	0.746	1.186	0.173	6.873	***
dem65	y7	0.824	1.280	0.161	7.925	***
dem65	y8	0.828	1.266	0.164	7.704	***

sem_paths(fit)

Regression Paths
DV	Predictor	Beta	B	SE	z	sig
dem60	ind60	0.447	1.483	0.400	3.708	***
dem65	ind60	0.182	0.572	0.235	2.432
dem65	dem60	0.885	0.837	0.099	8.419	***

sem_factorcor(fit, factors = factors)

Latent Factor Correlations
Factor 1	Factor 2	r	sig

sem_rsquared(fit)

R-Squared Values
Variable	R-Squared
x1	0.8461294
x2	0.9467924
x3	0.7606258
y1	0.7232244
y2	0.5142639
y3	0.5217888
y4	0.7152247
y5	0.6528919
y6	0.5565269
y7	0.6784379
y8	0.6853214
dem60	0.1995524
dem65	0.9609950

Diagram Output

semPaths(fit, whatLabels = "std", edge.label.cex = .5, layout = "tree2", rotation = 2, style = "lisrel", intercepts = FALSE, residuals = TRUE, curve = 1, curvature = 3, nCharNodes = 8, sizeMan = 6, sizeMan2 = 3, optimizeLatRes = TRUE, edge.color = "#000000", latents = factors)

Residual Correlation Matrix

sem_residuals(fit)

	x1	x2	x3	y1	y2	y3	y4	y5	y6	y7
x1
x2	0.00
x3	0.00	0.00
y1	0.03	-0.05	-0.09
y2	-0.08	-0.06	-0.07	0.00
y3	0.03	0.00	-0.06	0.06	-0.06
y4	0.12	0.08	0.06	-0.03	0.02	0.00
y5	0.13	0.07	0.02	-0.02	-0.01	0.01	-0.01
y6	-0.05	-0.06	-0.04	0.04	0.03	-0.09	0.05	-0.04
y7	-0.05	-0.06	-0.06	-0.01	0.01	0.00	0.01	0.01	0.00
y8	0.02	-0.01	-0.05	-0.01	0.04	-0.05	0.03	-0.04	0.01	0.03

Full Output

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

## lavaan 0.6-3 ended normally after 83 iterations
## 
##   Optimization method                           NLMINB
##   Number of free parameters                         42
## 
##   Number of observations                            75
##   Number of missing patterns                         1
## 
##   Estimator                                         ML
##   Model Fit Test Statistic                      37.617
##   Degrees of freedom                                35
##   P-value (Chi-square)                           0.350
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic              720.912
##   Degrees of freedom                                55
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.996
##   Tucker-Lewis Index (TLI)                       0.994
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -1547.791
##   Loglikelihood unrestricted model (H1)      -1528.728
## 
##   Number of free parameters                         42
##   Akaike (AIC)                                3179.582
##   Bayesian (BIC)                              3276.916
##   Sample-size adjusted Bayesian (BIC)         3144.543
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.032
##   90 Percent Confidence Interval          0.000  0.091
##   P-value RMSEA <= 0.05                          0.629
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.041
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Observed information based on                Hessian
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   ind60 =~                                                              
##     x1                1.000                               0.670    0.920
##     x2                2.180    0.140   15.580    0.000    1.460    0.973
##     x3                1.819    0.153   11.869    0.000    1.218    0.872
##   dem60 =~                                                              
##     y1                1.000                               2.223    0.850
##     y2                1.257    0.187    6.730    0.000    2.794    0.717
##     y3                1.058    0.149    7.083    0.000    2.351    0.722
##     y4                1.265    0.152    8.335    0.000    2.812    0.846
##   dem65 =~                                                              
##     y5                1.000                               2.103    0.808
##     y6                1.186    0.173    6.873    0.000    2.493    0.746
##     y7                1.280    0.161    7.925    0.000    2.691    0.824
##     y8                1.266    0.164    7.704    0.000    2.662    0.828
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   dem60 ~                                                               
##     ind60             1.483    0.400    3.708    0.000    0.447    0.447
##   dem65 ~                                                               
##     ind60             0.572    0.235    2.432    0.015    0.182    0.182
##     dem60             0.837    0.099    8.419    0.000    0.885    0.885
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .y1 ~~                                                                 
##    .y5                0.624    0.371    1.679    0.093    0.624    0.296
##  .y2 ~~                                                                 
##    .y4                1.313    0.703    1.867    0.062    1.313    0.273
##    .y6                2.153    0.731    2.944    0.003    2.153    0.356
##  .y3 ~~                                                                 
##    .y7                0.795    0.625    1.271    0.204    0.795    0.191
##  .y4 ~~                                                                 
##    .y8                0.348    0.461    0.755    0.450    0.348    0.109
##  .y6 ~~                                                                 
##    .y8                1.356    0.576    2.355    0.019    1.356    0.338
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .x1                5.054    0.085   59.724    0.000    5.054    6.943
##    .x2                4.792    0.174   27.472    0.000    4.792    3.194
##    .x3                3.558    0.162   21.918    0.000    3.558    2.548
##    .y1                5.465    0.304   17.983    0.000    5.465    2.090
##    .y2                4.256    0.453    9.398    0.000    4.256    1.093
##    .y3                6.563    0.378   17.344    0.000    6.563    2.016
##    .y4                4.453    0.386   11.520    0.000    4.453    1.339
##    .y5                5.136    0.303   16.977    0.000    5.136    1.974
##    .y6                2.978    0.389    7.665    0.000    2.978    0.891
##    .y7                6.196    0.380   16.317    0.000    6.196    1.897
##    .y8                4.043    0.374   10.816    0.000    4.043    1.257
##     ind60             0.000                               0.000    0.000
##    .dem60             0.000                               0.000    0.000
##    .dem65             0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .x1                0.082    0.020    4.109    0.000    0.082    0.154
##    .x2                0.120    0.070    1.701    0.089    0.120    0.053
##    .x3                0.467    0.090    5.198    0.000    0.467    0.239
##    .y1                1.891    0.472    4.008    0.000    1.891    0.277
##    .y2                7.373    1.355    5.442    0.000    7.373    0.486
##    .y3                5.067    0.975    5.198    0.000    5.067    0.478
##    .y4                3.148    0.761    4.137    0.000    3.148    0.285
##    .y5                2.351    0.492    4.778    0.000    2.351    0.347
##    .y6                4.954    0.901    5.495    0.000    4.954    0.443
##    .y7                3.431    0.733    4.683    0.000    3.431    0.322
##    .y8                3.254    0.712    4.572    0.000    3.254    0.315
##     ind60             0.448    0.087    5.135    0.000    1.000    1.000
##    .dem60             3.956    0.951    4.160    0.000    0.800    0.800
##    .dem65             0.172    0.222    0.778    0.437    0.039    0.039

modificationIndices(fit, sort.=TRUE, minimum.value=3)

##      lhs op rhs    mi    epc sepc.lv sepc.all sepc.nox
## 52 ind60 =~  y4 4.796  0.862   0.577    0.174    0.174
## 53 ind60 =~  y5 4.456  0.835   0.559    0.215    0.215
## 70 dem65 =~  y4 4.260  1.420   2.986    0.898    0.898
## 99    y1 ~~  y3 3.771  0.849   0.849    0.274    0.274
## 74    x1 ~~  y2 3.040 -0.155  -0.155   -0.200   -0.200

Descriptives

Correlation Matrix

CFA

Summary Output

Diagram Output

Residual Correlation Matrix

Full Output

SEM

Summary Output

Diagram Output

Residual Correlation Matrix

Full Output

Contents