SMHS BigDataBigSci SEM Ex1 - Revision history

Imoubara: /* Output */

2016-05-23T13:51:27Z

‎Output

Imoubara: /* Structural Equation Modeling (SEM) - Hands-on Example 1 (School Kids Mental Abilities) */

2016-05-23T13:40:14Z

‎Structural Equation Modeling (SEM) - Hands-on Example 1 (School Kids Mental Abilities)

Imoubara at 13:39, 23 May 2016

2016-05-23T13:39:33Z

Imoubara at 19:44, 18 May 2016

2016-05-18T19:44:37Z

Pineaumi: /* Structural Equation Modeling (SEM) - Hands-on Example 1 (School Kids Mental Abilities) */

2016-05-16T16:46:28Z

‎Structural Equation Modeling (SEM) - Hands-on Example 1 (School Kids Mental Abilities)

Pineaumi: /* Structural Equation Modeling (SEM) - Hands-on Example 1 (School Kids Mental Abilities) */

2016-05-16T16:44:52Z

‎Structural Equation Modeling (SEM) - Hands-on Example 1 (School Kids Mental Abilities)

Pineaumi: /* Structural Equation Modeling (SEM) - Hands-on Example 1 (School Kids Mental Abilities) */

2016-05-16T16:43:22Z

‎Structural Equation Modeling (SEM) - Hands-on Example 1 (School Kids Mental Abilities)

Imoubara at 15:55, 16 May 2016

2016-05-16T15:55:29Z

Imoubara at 15:53, 16 May 2016

2016-05-16T15:53:20Z

Imoubara at 15:51, 16 May 2016

2016-05-16T15:51:13Z

@@ Line 265: / Line 265: @@
 This only shows the factor loadings are shown but 3 additional columns with standardized values are added.
-<li>In the first column <b>(std.lv)</b>, only the latent variables have been standardized; </li>
+*In the first column <b>(std.lv)</b>, only the latent variables have been standardized;
-<li>In the second column <b>(std.all)</b>, both the latent and the observed variables have been standardized; </li>
+*In the second column <b>(std.all)</b>, both the latent and the observed variables have been standardized;
-<li> In the third column <b>(std.nox)</b>, both the latent and the observed variables have been standardized, except for the exogenous observed variables. This option may be useful if the standardization of exogenous observed variables has little meaning (for example, binary covariates). Since there are no exogenous covariates in this model, the last two columns are identical in this output.</li>
+* In the third column <b>(std.nox)</b>, both the latent and the observed variables have been standardized, except for the exogenous observed variables. This option may be useful if the standardization of exogenous observed variables has little meaning (for example, binary covariates). Since there are no exogenous covariates in this model, the last two columns are identical in this output.
   <b>library("semPlot")

@@ Line 69: / Line 69: @@
 To fully identify the model we need to set the metric of the latent variables. There are 2 ways to do this:
-<li>for each latent variable, fix the factor loading of one of the indicators (typically the first) to a constant (e.g., 1.0), or </li>
+*for each latent variable, fix the factor loading of one of the indicators (typically the first) to a constant (e.g., 1.0), or
-<li> standardize the variances of the 3 latent variables. </li>
+*standardize the variances of the 3 latent variables.
 Either way, we fix 3 of these 24 parameters, and 21 parameters remain free.

@@ Line 3: / Line 3: @@
 These data (Holzinger & Swineford 1939) include mental ability test scores of 7 & 8 grade children from two schools (Pasteur and Grant-White). This version of the dataset includes only 9 (out of the 26) tests. We can build and test a confirmatory factor analysis (CFA) SEM model for 3 correlated latent variables (or factors), each with three indicators:
-<li> <u>'''visual'''</u> factor measured by 3 variables: x1, x2 and x3,</li>
+*<u>'''visual'''</u> factor measured by 3 variables: x1, x2 and x3,
-<li> <u>'''textual'''</u> factor measured by 3 variables: x4, x5 and x6,</li>
+*<u>'''textual'''</u> factor measured by 3 variables: x4, x5 and x6,
-<li> <u>'''speed'''</u> factor measured by 3 variables: x7, x8 and x9.</li>
+*<u>'''speed'''</u> factor measured by 3 variables: x7, x8 and x9.
 <center>
@@ Line 142: / Line 142: @@
 ===Core Lavaan Methods===
-<li> <b>summary</b>() print a long summary of the model results</li>
+*<b>summary</b>() print a long summary of the model results
-<li><b>show</b>() print a short summary of the model results</li>
+*<b>show</b>() print a short summary of the model results
-<li> <b>coef</b>() returns the estimates of the free parameters in the model as a named numeric vector</li>
+*<b>coef</b>() returns the estimates of the free parameters in the model as a named numeric vector
-<li> <b>fitted</b>() returns the implied moments (covariance matrix and mean vector) of the model</li>
+*<b>fitted</b>() returns the implied moments (covariance matrix and mean vector) of the model
-<li> <b>resid</b>() returns the raw, normalized or standardized residuals (difference between implied and observed moments)</li>
+*<b>resid</b>() returns the raw, normalized or standardized residuals (difference between implied and observed moments)
-<li> <b>vcov</b>() returns the covariance matrix of the estimated parameters</li>
+*<b>vcov</b>() returns the covariance matrix of the estimated parameters
-<li><b>predict</b>() compute factor scores</li>
+*<b>predict</b>() compute factor scores
-<li> <b>logLik</b>() returns the log-likelihood of the fitted model (if maximum likelihood estimation was used)</li>
+*<b>logLik</b>() returns the log-likelihood of the fitted model (if maximum likelihood estimation was used)
-<li> <b>AIC</b>(), BIC() compute information criteria (if maximum likelihood estimation is used)</li>
+*<b>AIC</b>(), BIC() compute information criteria (if maximum likelihood estimation is used)
-<li> <b>update</b>() update a fitted lavaan object</li>
+*<b>update</b>() update a fitted lavaan object
-<li> <b>inspect</b>() peek into the internal representation of the model; by default, it returns a list of model matrices counting the free parameters in the model; can also be used to extract starting values, gradient values, and much more</li>
+*<b>inspect</b>() peek into the internal representation of the model; by default, it returns a list of model matrices counting the free parameters in the model; can also be used to extract starting values, gradient values, and much more
 If these args are set to TRUE, the output includes additional fit measures, standardized estimates, and R2 values for the dependent variables, respectively
@@ Line 169: / Line 169: @@
 The output consists of three sections.
-<li> The <b>first section</b> (first 6 lines) contains the package version number, an indication whether the model has converged (and in how many iterations), and the effective number of observations used in the analysis.</li>
+*The <b>first section</b> (first 6 lines) contains the package version number, an indication whether the model has converged (and in how many iterations), and the effective number of observations used in the analysis.
-<li>The <b>second section</b> contains the model χ^2 test statistic, degrees of freedom, and a p value are printed. If fit.measures = TRUE, it also prints the test statistic of the baseline model (where all observed variables are assumed to be uncorrelated) and several popular fit indices. If maximum likelihood estimation is used, this section will also contain information about the log-likelihood, the AIC, and the BIC. </li>
+*The <b>second section</b> contains the model χ^2 test statistic, degrees of freedom, and a p value are printed. If fit.measures = TRUE, it also prints the test statistic of the baseline model (where all observed variables are assumed to be uncorrelated) and several popular fit indices. If maximum likelihood estimation is used, this section will also contain information about the log-likelihood, the AIC, and the BIC.
-<li>The <b>third section</b> provides an overview of the parameter estimates, including the type of standard errors used and whether the observed or expected information matrix was used to compute standard errors. Then, for each model parameter, the estimate and the standard error are displayed, and if appropriate, a z value based on the Wald test and a corresponding two-sided p value are also shown. To ease the reading of the parameter estimates, they are grouped into three blocks:</li>
+*The <b>third section</b> provides an overview of the parameter estimates, including the type of standard errors used and whether the observed or expected information matrix was used to compute standard errors. Then, for each model parameter, the estimate and the standard error are displayed, and if appropriate, a z value based on the Wald test and a corresponding two-sided p value are also shown. To ease the reading of the parameter estimates, they are grouped into three blocks:
-<li>factor loadings, </li>
+*factor loadings,
-<li> factor covariances, and </li>
+*factor covariances, and
-<li>residual variances of both observed variables and factors.</li>
+*residual variances of both observed variables and factors.</li>
 The <b>summary</b>() method provides a nice summary of the model results for visualization purposes. The <b>parameterEstimates</b>() method returns the actual parameter estimates as a <b>data.frame</b>, which can be processed further.

@@ Line 66: / Line 66: @@
 These <b>12 parameters</b> are represented in the path diagram as single-headed and double-headed arrows, respectively. We also need to estimate the residual variances of the 9 observed variables and the variances of the 3 latent variables, resulting in <b>12 additional free parameters</b>. In total, we have <b>24 parameters.</b>
-[[Image:SMHS_BigDataBigSci2.png|200px]]
+<center>[[Image:SMHS_BigDataBigSci2.png|200px]]</center>
 To fully identify the model we need to set the metric of the latent variables. There are 2 ways to do this:

@@ Line 83: / Line 83: @@
 Since these data contain 3 latent variables, and no regressions, the minimalist syntax is:
-  <b>data.model <- 'visual 	=~ x1 + x2 + x3
+  <b>data.model <- 'visual 	        =~ x1 + x2 + x3
   textual 	                =~ x4 + x5 + x6
   speed 	                        =~ x7 + x8 + x9'</b>

@@ Line 10: / Line 10: @@
 {| class="wikitable" style="text-align:center; " border="1"
 |-
-|ID||lhs||op||rhs||user||free||ustart
+|<b>id</b>||<b>lhs</b>||<b>op</b>||<b>rhs</b>||<b>user</b>||<b>free</b>||<b>ustart</b>
 |-
 |1 ||Visual||=~||x1||1||0||1

@@ Line 69: / Line 69: @@
 To fully identify the model we need to set the metric of the latent variables. There are 2 ways to do this:
-* for each latent variable, fix the factor loading of one of the indicators (typically the first) to a constant (e.g., 1.0), or
+<li>for each latent variable, fix the factor loading of one of the indicators (typically the first) to a constant (e.g., 1.0), or </li>
-* standardize the variances of the 3 latent variables.
+<li> standardize the variances of the 3 latent variables. </li>
 Either way, we fix 3 of these 24 parameters, and 21 parameters remain free.
@@ Line 142: / Line 142: @@
 ===Core Lavaan Methods===
-* <b>summary</b>() print a long summary of the model results
+<li> <b>summary</b>() print a long summary of the model results<li/>
-* <b>show</b>() print a short summary of the model results
+<li><b>show</b>() print a short summary of the model results<li/>
-* <b>coef</b>() returns the estimates of the free parameters in the model as a named numeric vector
+<li> <b>coef</b>() returns the estimates of the free parameters in the model as a named numeric vector<li/>
-* <b>fitted</b>() returns the implied moments (covariance matrix and mean vector) of the model
+<li> <b>fitted</b>() returns the implied moments (covariance matrix and mean vector) of the model<li/>
-* <b>resid</b>() returns the raw, normalized or standardized residuals (difference between implied and observed moments)
+<li> <b>resid</b>() returns the raw, normalized or standardized residuals (difference between implied and observed moments)<li/>
-* <b>vcov</b>() returns the covariance matrix of the estimated parameters
+<li> <b>vcov</b>() returns the covariance matrix of the estimated parameters<li/>
-* <b>predict</b>() compute factor scores
+<li><b>predict</b>() compute factor scores<li/>
-* <b>logLik</b>() returns the log-likelihood of the fitted model (if maximum likelihood estimation was used)
+<li> <b>logLik</b>() returns the log-likelihood of the fitted model (if maximum likelihood estimation was used)<li/>
-* <b>AIC</b>(), BIC() compute information criteria (if maximum likelihood estimation is used)
+<li> <b>AIC</b>(), BIC() compute information criteria (if maximum likelihood estimation is used)<li/>
-* <b>update</b>() update a fitted lavaan object
+<li> <b>update</b>() update a fitted lavaan object<li/>
-* <b>inspect</b>() peek into the internal representation of the model; by default, it returns a list of model matrices counting the free parameters in the model; can also be used to extract starting values, gradient values, and much more
+<li> <b>inspect</b>() peek into the internal representation of the model; by default, it returns a list of model matrices counting the free parameters in the model; can also be used to extract starting values, gradient values, and much more<li/>
 If these args are set to TRUE, the output includes additional fit measures, standardized estimates, and R2 values for the dependent variables, respectively
@@ Line 169: / Line 169: @@
 The output consists of three sections.
-* The <b>first section</b> (first 6 lines) contains the package version number, an indication whether the model has converged (and in how many iterations), and the effective number of observations used in the analysis.
+<li> The <b>first section</b> (first 6 lines) contains the package version number, an indication whether the model has converged (and in how many iterations), and the effective number of observations used in the analysis.<li/>
-*The <b>second section</b> contains the model χ^2 test statistic, degrees of freedom, and a p value are printed. If fit.measures = TRUE, it also prints the test statistic of the baseline model (where all observed variables are assumed to be uncorrelated) and several popular fit indices. If maximum likelihood estimation is used, this section will also contain information about the log-likelihood, the AIC, and the BIC.
+<li>The <b>second section</b> contains the model χ^2 test statistic, degrees of freedom, and a p value are printed. If fit.measures = TRUE, it also prints the test statistic of the baseline model (where all observed variables are assumed to be uncorrelated) and several popular fit indices. If maximum likelihood estimation is used, this section will also contain information about the log-likelihood, the AIC, and the BIC. <li/>
-*The <b>third section</b> provides an overview of the parameter estimates, including the type of standard errors used and whether the observed or expected information matrix was used to compute standard errors. Then, for each model parameter, the estimate and the standard error are displayed, and if appropriate, a z value based on the Wald test and a corresponding two-sided p value are also shown. To ease the reading of the parameter estimates, they are grouped into three blocks:
+<li>The <b>third section</b> provides an overview of the parameter estimates, including the type of standard errors used and whether the observed or expected information matrix was used to compute standard errors. Then, for each model parameter, the estimate and the standard error are displayed, and if appropriate, a z value based on the Wald test and a corresponding two-sided p value are also shown. To ease the reading of the parameter estimates, they are grouped into three blocks:<li/>
-* factor loadings,
+<li>factor loadings, </li>
-* factor covariances, and
+<li> factor covariances, and </li>
-* residual variances of both observed variables and factors.
+<li>residual variances of both observed variables and factors.</li>
 The <b>summary</b>() method provides a nice summary of the model results for visualization purposes. The <b>parameterEstimates</b>() method returns the actual parameter estimates as a <b>data.frame</b>, which can be processed further.
@@ Line 265: / Line 265: @@
 This only shows the factor loadings are shown but 3 additional columns with standardized values are added.
-* In the first column <b>(std.lv)</b>, only the latent variables have been standardized;
+<li>In the first column <b>(std.lv)</b>, only the latent variables have been standardized; </li>
-* In the second column <b>(std.all)</b>, both the latent and the observed variables have been standardized;
+<li>In the second column <b>(std.all)</b>, both the latent and the observed variables have been standardized; </li>
-* In the third column <b>(std.nox)</b>, both the latent and the observed variables have been standardized, except for the exogenous observed variables. This option may be useful if the standardization of exogenous observed variables has little meaning (for example, binary covariates). Since there are no exogenous covariates in this model, the last two columns are identical in this output.
+<li> In the third column <b>(std.nox)</b>, both the latent and the observed variables have been standardized, except for the exogenous observed variables. This option may be useful if the standardization of exogenous observed variables has little meaning (for example, binary covariates). Since there are no exogenous covariates in this model, the last two columns are identical in this output.</li>
   <b>library("semPlot")

@@ Line 3: / Line 3: @@
 These data (Holzinger & Swineford 1939) include mental ability test scores of 7 & 8 grade children from two schools (Pasteur and Grant-White). This version of the dataset includes only 9 (out of the 26) tests. We can build and test a confirmatory factor analysis (CFA) SEM model for 3 correlated latent variables (or factors), each with three indicators:
-* visual factor measured by 3 variables: x1, x2 and x3,
+<li> visual factor measured by 3 variables: x1, x2 and x3,</li>
-* textual factor measured by 3 variables: x4, x5 and x6,
+<li> textual factor measured by 3 variables: x4, x5 and x6,</li>
-* speed factor measured by 3 variables: x7, x8 and x9.
+<li>speed factor measured by 3 variables: x7, x8 and x9.</li>
 <center>