Analysis Parameters

Click the Set parameters button on the Advanced tab of the Structural Equation Modeling Startup Panel to display the Analysis Parameters dialog box. Note that you can also access this dialog box by clicking the Parameters button on the Path Construction Tool or the Set Parameters button on the Model tab of the Monte Carlo Analysis dialog box.

Data to analyze. Use the options under Data to analyze to select which type of data to analyze. For standard path analyses or structural equation models, you choose either Covariances or Correlations, for models specifying intercepts, or structured means, you must specify the Moments option.

Covariances. Select the Covariances option button to analyze the covariance matrix of the input variables, regardless of what kind of data are input. So, for example, if you input a correlation matrix file with standard deviations, STATISTICA will calculate the covariance matrix and analyze it.  If your input file is a covariance matrix file, STATISTICA will analyze it directly.  If your file contains raw data, STATISTICA will analyze it and calculate the covariance matrix for you. See also, Covariance Matrices vs. Correlation Matrices for information on how STATISTICA analyzes these two types of matrices.

Correlations. Select the Correlations option button to calculate the correlation matrix from the input data and analyze it. STATISTICA analyzes the correlation matrix correctly, using constrained estimation theory developed by Michael Browne (see Browne, 1982; Mels, 1989; Browne & Mels, 1992), and implemented first in the computer program RAMONA. As a result, STATISTICA gives the correct standard errors, estimates, and test statistics when a correlation matrix is analyzed directly. When combined with the Standardization - New option STATISTICA can estimate a completely standardized path model, where all variables are standardized to have unit variance, and standard errors can be estimated as well.

Moments. Select the Moments option button to analyze the augmented product-moment matrix instead of the covariance matrix. This option is selected if you are analyzing models involving intercepts or structured means. STATISTICA will also add, to the input variable list, an additional variable called CONSTANT that always takes on the value 1. CONSTANT is a dummy variable used to represent means in structured means models, i.e., those with an intercept variable.

Output options. Use the options in the Output options frame for preliminary control over the appearance of your output. You can preselect the number of decimal places to be printed in report editor, and you can select whether or not to print estimated standard errors for model coefficients.

No.  of decimal places. Enter a number between 1 and 6 in the No. of decimal places field. The number is number of decimal places displayed by default in the results spreadsheets.  

Standard errors. Select the Standard errors check box to display estimated standard errors for all parameters in the PATH1 text output, and Model Summary Spreadsheet. Note that if OLS estimation is performed, or the "old" standardization method is employed, standard errors will not be available.

Convergence criteria. Use the options in the Convergence criteria frame to adjust constants that can directly affect when the program decides convergence has occurred during iteration. The default values produce desirable results for a wide variety of problems, and you will seldom need to adjust these criteria.

Max. residual cosine. Enter a value for the maximum residual cosine in the Max. residual cosine field. This criterion becomes small when parameter values have stabilized. You can alter this criterion in the input field. The default value of .0001 works well across a wide variety of situations. For a technical definition of this criterion and a discussion of its merits, see the discussion of Unconstrained Minimization Techniques.

Relative funct. change. Enter a value for the relative function change in the Relative funct. change field. This criterion becomes small when the discrepancy function being minimized (see the section on Statistical Estimation Theory for a discussion) is no longer changing. On occasion, especially when boundary cases are encountered, it will not be possible for the program to iterate to a point where a local or global minimum is obtained. In that case, the Maximum Residual Cosine criterion may not fall below, but the discrepancy function will not change. At that point, this criterion will stop iteration. In general, it should be kept very low, or it may cause iteration to terminate prematurely.  For a technical definition of the criterion see the discussion of Unconstrained Minimization Techniques.

Discrepancy function. Use the options in the Discrepancy function frame to specify which discrepancy function or functions will be minimized to yield parameter estimates. Consult the section on Statistical Estimation for an in-depth discussion of these methods.

Maximum Likelihood (ML). Select the Maximum Likelihood (ML) button to perform Maximum Wishart Likelihood estimation if Correlations or Covariances are analyzed, and Maximum Normal Likelihood estimation if Moments are analyzed.  

Generalized Least Squares (GLS). Select the Generalized Least Squares (GLS) button to perform Generalized Least Squares estimation.

GLS --> ML. Select the GLS--> ML (GLS followed by ML) option button to perform five iterations using the Generalized Least Squares estimation procedure followed by Maximum Likelihood Estimation. If selected, this option disregards the current settings in the Maximum No. of Iterations field.

Ordinary Least Squares (OLS). Select the Ordinary Least Squares (OLS) option button to perform Ordinary Least Squares estimation.

ADFG. Select the ADFG option button to perform Asymptotically Distribution Free (Gramian) estimation, which does not require the assumption of multivariate normality. In this variant, the weight matrix is guaranteed to be Gramian. As a preliminary to ADFG estimation, STATISTICA performs GLS estimation.

ADFU. Select the Asymptotically Distribution Free Unbiased (ADFU) option button to perform Asymptotically Distribution Free (Unbiased) estimation, which does not require the assumption of multivariate normality. In this variant, the weight matrix is an unbiased estimate of the true weight matrix. However, this estimated matrix may not be Gramian (i.e., invertible) in all cases. If it is not, STATISTICA gives an error message. At that point, you should restart the estimation using the ADFG option. As a preliminary to ADFU estimation, STATISTICA performs GLS estimation.

Global iteration parameters. Use the options under Global iteration parameters to enter parameters that control the basic iterative process. For a technical description of the iteration process, see Unconstrained Minimization Techniques.

Maximum no. of iterations. Enter the maximum number of iterations allowed in the Maximum no. of iterations field. The default number is 30. When this number of iterations is reached, the iterative process will automatically terminate, and a message will be issued to indicate that the maximum number of iterations was exceeded. Minimum is zero (in which case the discrepancy function and estimated covariance matrix will be computed, and control will be returned to the user), maximum is 1000.

Maximum step length. Enter the maximum length of the step vector that will be allowed in the Maximum step length field. See Unconstrained Minimization Techniques for a discussion of this parameter. See the Solving Iteration Problems for suggestions on how to use this parameter to solve some problems encountered during iteration.

Steepest descent iterations. Enter a number of steepest descent iterations to proceed the standard iterations in the Steepest descent iterations field. See Solving Iteration Problems for suggestions on how to use this parameter to solve some problems encountered during iteration.

Step tolerance. Enter a tolerance value in the Step tolerance field. STATISTICA uses this value for when a parameter is temporarily eliminated from the iterative process. The tolerance value is basically one minus the squared multiple correlation of a parameter with the other parameters. If a parameter becomes highly redundant with other parameters during iteration, the approximate Hessian employed during Gauss-Newton iteration becomes unstable. This parameter controls when a parameter is temporarily removed from the iterative process. Very low values of this parameter mean that a parameter will never be removed. This can cause iteration to "blow up" if the approximate Hessian becomes nearly singular.  High Values mean that parameters will not be varied while they are moderately correlated with other parameters. This can cause iteration to fail if parameters are fairly highly correlated at the solution point. Change this parameter seldom, and in small increments. The default value seems to work well on a wide range of problems.

Initial values. Use the options in the Initial values frame to select the method employed to find initial values for free parameters. The default method uses .5 for all free parameters, except variances and covariances (or correlations) of manifest exogenous variables. These parameters are initialized at the values obtained from the sample data.

Default. Select the Default option button to use .5 for all free parameters, except variances and covariances (or correlations) of manifest exogenous variables. These parameters are initialized at the values obtained from the sample data.

Automatic. Select the Automatic option button to obtain the initial values via a method that is a minor adaptation of the technique described by McDonald and Hartmann (1992).

Standardization. Use the options under Standardization to choose to generate either a standardized solution (where latent variables all have unit variance) by one of two methods, or an unstandardized solution.

Note that the New and Old options will cause the program to compute standardized solutions based on the (standardized) endogenous latent variables (this is the common practice in most programs of this kind); if your model does not contain latent endogenous variables (e.g., only contains manifest exogenous variables), these methods of standardization may not be appropriate, and you may want to use a correlation matrix as input instead, and choose the New method to obtain estimates that are standardized in the manifest exogenous variables. See also, New Method for Standardizing Endogenous Latent Variables in the Technical Aspects of SEPATH section for additional details.

New. Check the New option button to estimate a standardized solution via constrained estimation. This approach produces a solution where all latent variables, both independent and dependent, have variances of 1. Unlike the old method, however, standard errors are available with this option. Combining this option with the Data to Analyze - Correlations option (see above) allows one to estimate a completely standardized path model, where all variables, manifest and latent, have unit variances, and standard errors can be estimated for all parameters.

Old. Check the Old option button to estimate a standardized solution using older methods. Older programs generate a standardized solution after iteration is complete, then perform a calculation after the fact to transform the solution to a standardized form. This method gets a solution faster than the New option described above, because it does not need to use constrained estimation. However, standard errors cannot be computed.

None. Check the None option button to calculate an unstandardized solution.

Manifest exogenous. Use the options under Manifest exogenous to account for exogenous manifest variables. Most models do not have manifest variables that are exogenous. If a model does have such variables, their variances and covariances must be accounted for. In most cases (but not all), the variances and covariances estimated under one of the standard estimation techniques will be identical to the observed variances and covariances, and consequently these parameters are not of much interpretive interest. STATISTICA provides two approaches to calculating these parameters automatically and keeping them out of view (the Fixed and Free options below) and also allows them to be declared explicitly.

Free. Check the Free option button to treat the variances and covariances among the manifest exogenous variables as free parameters and add them to the model, although their values are not shown. Start values are the observed variances and covariances. If you select this option and attempt (in the PATH1 input) to specify the variance or covariance of a manifest exogenous variable, you will generate an error message.

Fixed. Check the Fixed option button to treat the variances and covariances for manifest exogenous variables as fixed (at the value of the observed variances and covariances) during iteration. After iteration, they are treated as if they were free parameters. This approach eliminates, in the case of several manifest exogenous variables, the addition of a number of extra free parameters, which can slow down iteration and make it less reliable. The user should take the output obtained by this approach, and resubmit it using the Free option described below to guarantee correct estimates. If you select this option and attempt (in the PATH1 input) to specify the variance or covariance of a manifest exogenous variable, you will generate an error message.

User. Check the User option button if you want to specify the variances and covariances of all manifest exogenous variables, using standard PATH1 syntax.

Line search method. Use the options under Line search method to choose a basic line search method. Once the step direction has been chosen, the minimization problem is basically reduced from a problem in n unknowns to a problem in 1 unknown, i.e., the length of the step. There are three methods for choosing the length of the step.  Their technical aspects are discussed in the section on Unconstrained Minimization Techniques.

Cubic interpolation. Check the Cubic interpolation option button to use cubic interpolation, a method that is reasonably fast and rather robust. It works well in the vast majority of circumstances.

Golden section. Check the Golden section option button to use golden section, a method that tries to solve the one dimensional minimization problem exactly on each iteration. It often converges in slightly fewer iterations than cubic interpolation, but takes longer, because it requires more function evaluations on each iteration.

Simple stephalving. Check the Simple stephalving option button to use simple stephalving. Although this is the fastest method, it will fail to converge for a fair number of problems that the other two, more sophisticated methods succeed on.

Line search parameters. Use the options under Line search parameters to choose numerical parameters that control the performance of the line search method you have chosen. Only a subset of the parameters are relevant to each line search method. Only relevant parameters will be enabled for the currently selected line search method.

Max. no. of stephalves. Enter a value in the Max. no. of stephalves field to set the maximum number of stephalves allowed on a single iteration if the Simple Stephalving line search method is used.

Stephalve fraction. Enter a value in the Stephalve fraction field to set the fraction the current step is multiplied by when Simple Stephalving is used as the line search method.

Cubic LS alpha. Enter a value in the Cubic LS alpha field to control how large a reduction in the discrepancy function  has to be made before a step is considered acceptable when the Cubic Interpolation line search method is used. The default value, .0001, allows virtually any improvement to be considered acceptable.

Golden search tau. Enter a value in the Golden search aau field to control how wide a range to which the Golden Section line search is limited.

Golden srch precision. Enter a value in the Golden srch precision field to control the precision of estimation in a Golden Section line search.