EViews Help: Factor

Each of the following takes an optional argument “(0)” (e.g., “@params(0)”). If no argument is provided, the data member returns the value for the estimated factor specification. If the optional argument is provided, the member returns the value for the independence (zero factor) model.

@params[(0)] number of estimated parameters.

@ncoefs[(0)] same as @parms.

@objective[(0)] value of the objective function in factor extraction.

@discrep[(0] same as @objective.

@aic[(0] Akaike Information Criterion.

@sc[(0)] Schwarz Information Criterion.

@hq[(0)] Hannan-Quinn Information Criterion.

@ecvi[(0)] Expected Cross-validation Index.

@chisq[(0)] Chi-square test statistic for model adequacy.

@chisqdf[(0)] Degrees of freedom for the chi-square statistic.

@chisqprob[(0)] p-value for the chi-square statistic

@bartlett[(0)] Bartlett’s adjusted version of the Chi-square test statistic.

@bartlettprob[(0)] p-value for Bartlett’s adjusted version of the chi-square statistic.

@rmsr[(0)] Root mean square residuals.

@srmsr[(0)] Standardized root mean square residuals.

@gfi[(0)] Jöreskog and Sörbom Generalized Fit Index.

@agfi[(0)] Jöreskog and Sörbom Adjusted Generalized Fit Index.

@noncent[(0)] Noncentrality parameter.

@gammahat[(0)] Gamma hat non-centrality.

@mdnoncent[(0)] McDonald non-centrality.

@rmsea[(0)] Root MSE approximation.

Vectors and Matrices for Model

@obsmat matrix of number of observations used for each pair of variables.

@cov observed covariance or correlation matrix.

@scaled scaled covariance matrix.

@fitted fitted covariance matrix.

@common common variance fitted covariance matrix (fitted matrix with communality on the diagonal).

@resid residual matrix (observed–fitted).

@residcommon residual matrix using common variance.

@reduced reduced covariance matrix using final uniqueness estimates.

@ireduced reduced covariance matrix using initial uniqueness estimates.

@anticov Anti-image covariance matrix.

@partcor partial correlation matrix.

@iunique vector of initial uniqueness estimates.

@unique vector of final uniqueness estimates.

@icommunal vector initial communality estimates.

@communal vector of final communality estimates.

@rowadjust vector of row standardization terms (used to rescale results so that the uniqueness and communality estimates add up to the observed diagonals).

@loadings estimated loadings matrix.

@rloadings rotated loadings matrix.

@rotmat factor rotation matrix:

@rotmatinv loadings rotation matrix:

@factcor factor correlation matrix.

@factstruct factor structure matrix (correlation between factors and the variables).

String Values

@attr("arg") string containing the value of the arg attribute, where the argument is specified as a quoted string.

@command full command line form of the Factor estimation command. Note this is a combination of @method, @options, and @spec.

@description string containing the Factor object’s description (if available).

@detailedtype returns a string with the object type: “FACTOR”.

@displayname returns the Factor object’s display name. If the Factor object has no display name set, the name is returned.

@factnames factor names.

@method command line form of the Factor estimation method type.

@name returns the Factor object’s name.

@options command line form of estimation options.

@smpl sample used for estimation.

@spec original factor specification.

@type returns a string with the object type: “FACTOR”.

@updatetime returns a string representation of the time and date at which the Factor was last updated.

@varnames variable names.

Factor Examples

To declare a factor object named f1:

factor f1

To declare and estimate by maximum likelihood a factor object F2 using data in the group GROUP01:

factor f2.ml group01

To declare and estimate, using iterated principal factors, the factor object F3 using the sym matrix SYM01:

factor f3.ipf sym01 785

In addition to providing the name of the matrix, we indicate that the covariance is computed using 785 observations.

To estimate a factor model by ML using the series X1 X2 and X3 using a command:

factest x1 x2 x3

EViews will create an untitled factor object containing the results of the estimation.

anticov

Factor Views

Display the anti-image covariance matrix based on the observed covariance matrix

Syntax

factor_name.anticov(options)

The anti-image covariance is obtained by taking the inverse of the covariance matrix, and row and column scaling by the diagonals of the inverse.

The diagonal elements of the matrix are equal to 1 minus the squared multiple correlations (SMCs). The off-diagonal elements of the anti-image covariance are equal to the negative of the partial covariances multiplied by

, where

are the remaining variables.

Options

p	Print the matrix.

Examples

factor f1.ml group01

f1.anticov(p)

estimates the factor analysis object F1, then displays and prints the anti-image covariance matrix.

Cross-References

See “Observed Covariances”. See also Factor::observed, Factor::partcor, Factor::smc.

clearhist

Factor Procs

Clear the contents of the history attribute.

Removes the factor’s history attribute, as shown in the label view of the factor.

Syntax

factor_name.clearhist

Examples

f1.clearhist

f1.label

The first line removes the history from the factor F1, and the second line displays the label view of F1, including the now blank history field.

Cross-references

See “Labeling Objects” for a discussion of labels and display names.

See also copy.

display

Factor Views

Display table, graph, or spool output in the factor object window.

Display the contents of a table, graph, or spool in the window of the factor object.

Syntax

factor_name.display object_name

Examples

factor1.display tab1

Display the contents of the table TAB1 in the window of the object FACTOR1.

Cross-references

Most often used in constructing an EViews Add-in. See “Custom Object Output”.

displayname

Factor Procs

Set display name for factor object.

Attaches a display name to a factor object which may be used to label output in place of the standard factor object name.

Syntax

factor_name.displayname display_name

Display names are case-sensitive, and may contain a variety of characters, such as spaces, that are not allowed in object names.

Examples

f1.displayname Holzinger Example

The first line attaches a display name “Holzinger Example” to the factor object F1.

Cross-references

See “Labeling Objects” for a discussion of labels and display names. See also Factor::label.

eigen

Factor Views

Display table or graph of eigenvalues of observed, scaled observed, or reduced covariance matrix.

Syntax

factor_name.eigen(options)

By default, eigen will display a table of eigenvalues for the specified source matrix. You may add the option keywords “eigvec” and “matrix” to include additional output.

To display a graph of the results, you should some combination of the “scree”, “diff” and “cproport” option keywords.

Options

source=arg (default= “observed”)	Source matrix to be analyzed: “observed” (observed covariance matrix), “scaled” (scaled observed matrix), “reducedinit” (reduced using initial uniquenesses), “reduced” (reduced using final uniquenesses).
eigvec	Add the eigenvectors to the table of eigenvalue results. May be combined with the “matrix” keyword.
matrix	Display the source matrix along with the table of eigenvalue results. May be combined with the “eigvec” keyword.
scree	Display eigenvalue graph of the ordered eigenvalues (Scree plot). May be combined with the “diff” and “cproport” keywords.
diff	Display graph of the difference in successive eigenvalues. May be combined with the “scree” and “cproport” keywords.
cproport	Display graph of the cumulative proportion of total variance associated with each eigenvalue/eigenvector. May be combined with the “scree” and “diff” keywords.
prompt	Force the dialog to appear from within a program.
p	Print results.

Examples

f1.eigen(source=observed, scree)

displays the scree plot based on the observed covariance matrix.

f1.eigen(source=reducedinit, eigvec, matrix)

displays a table of eigenvalues and corresponding eigenvectors for the reduced covariance matrix (using the initial uniquenesses). The table also shows the reduced covariance matrix.

f1.eigen(source=reducedinit, scree, cproport, diff)

shows the scree, cumulative proportion, and eigenvalue difference graphs based on the reduced initial covariance.

Cross-references

See “Eigenvalues”.

factnames

Factor Procs

Specify names for the unobserved factors.

Assign names to the unobserved factors in an estimated factor object. These names will subsequently be used in table and graphical output.

Syntax

factor_name.factnames [name1 ...]

You should follow the keyword with a list of names for the factors. You may clear an existing set of factnames by using the factnames keyword with an empty list of factors.

Examples

f1.factnames Verbal Visual

attaches names “Verbal” and “Visual” to the first two retained factors. The names will be used in subsequent views and procedures.

f1.factnames

clears the existing list of factor names.

factor

Factor Declaration

Declare a factor object.

Syntax

factor factor_name

factor factor_name.method(options) specification

Follow the factor keyword with a name and an optional specification. If you wish to enter the specification, you should follow the new factor name with a period, an estimation method, and the factor analysis specification. Valid estimation methods are gls, ipf, ml, pace, pf, and uls. Refer to each method for a description of the available options.

Examples

factor f1.gls(n=map, priors=max) group01

declares the factor object F1 and estimates a factor model from the correlation matrix for the series in the group object GROUP01. The default method, Velicer’s MAP, is used for determining the number of factors.

factor fac1.ipf(n=2, maxit=4) var1 var2 var3 var4

creates the factor object FAC1 then extracts two factors from the variables VAR1–VAR4 by the iterative principal factor method, with a maximum of four iterations.

factor f2.ml group01

declares the factor object F2 then estimates the factor model using the correlation matrix for the series in GROUP01 by maximum likelihood method.

Cross-references

“Factor Analysis” provides basic information on factor analysis.

fitstats

Factor Views

Display Goodness-of-fit statistics for an estimated factor analysis object.

Syntax

factor_name.fitstats

Options

p	Print the results.

Examples

factor f1.ml group01

f1.fitstats(p)

estimates a factor model then displays and prints a table of Goodness-of-fit statistics.

Cross-references

See “Discrepancy and Chi-Square Tests”.

fitted

Factor Views

Display fitted and common covariances from a factor analysis object.

Syntax

factor_name.fitted(options)

Options

common	Display common covariance.(default is to display the fitted covariance).
p	Print the matrix.

Examples

factor f1.ml group01

f1.fitted(p)

estimates a factor model for the series in GROUP01, then displays and prints the fitted covariance matrix for the factor object F1.

f1.fitted(common)

displays the estimate of the fitted common variance.

Cross-references

See “Matrix Views”. See also Factor::reduced.

fsel	Factor Views

Display results of Bai and Ng or Ahn and Horenstein factor selection techniques.

Syntax

factor_name.fsel

Only relevant for factor models estimated using the “n=bn” or “n=ah” methods for determining the number of factors to retain.

Options

p	Print the results.

Examples

factor f1.ml(n=bn) group01

f1.fsel(p)

estimates a factor model using the Bai and Ng method for determining the number of factors, and then displays and prints a table of selection results.

Cross-references

See “Number of Factors” for discussion of methods for selecting the number of factors retained in factor analysis.

See “Bai and Ng” and “Ahn and Horenstein” for a discussion of these specific methods.

gls	Factor Methods

Generalized least squares estimation of the factor model.

Syntax

factor_name.gls(options) x1 [x2 x3...] [@partial z1 z2 z3...]

factor_name.gls(options) matrix_name [[obs] [conditioning]] [@ name1 name2 name3...]

The first method computes the observed dispersion matrix from a set of series or group objects. Simply append a period and the gls keyword to the name of your object, followed by the names of your series and groups, You may optionally use the keyword @partial and append a list of conditioning series.

In the second method you will provide the name of the observed dispersion matrix, and optionally, the number of observations and the rank of the set of conditioning variables. If the latter is not provided, it will be set to 1 (representing the constant in the standard centered variance calculations). You may also provide names for the columns of the correlation matrix by entering the @-sign followed by a list of valid series names.

Options

Estimation Options

rescale	Rescale the uniqueness and loadings estimates so that they match the observed variances.
maxit=integer	Maximum number of iterations.
conv=scalar	Set convergence criterion. The criterion is based upon the maximum of the percentage changes in the scaled estimates. The criterion will be set to the nearest value between 1e-24 and 0.2.
showopts / ‑showopts	[Do / do not] display the starting coefficient values and estimation options in the rotation output.
prompt	Force the dialog to appear from within a program.
p	Print basic estimation results.

Number of Factors Options

n=arg or fsmethod=arg (default=“map”)	Number of factors: “kaiser” (Kaiser-Guttman greater than mean), “mineigen” (Minimum eigenvalue criterion; specified using “eiglimit”), “varfrac” (fraction of variance accounted for; specified using “varlimit”), “map” (Velicer’s Minimum Average Partial method), “bstick” (comparison with broken stick distribution), “parallel” (parallel analysis: number of replications specified using “pnreps”; “pquant” indicates the quantile method value if employed), “scree” (standard error scree method), “bn” (Bai and Ng (2002)), “ah” (Ahn and Horenstein (2013)), integer (user-specified integer value).
eiglimit=number (default=1)	Limit value for retaining factors using the eigenvalue comparison (where “n=mineigen”).
varlimit=number (default=0.5)	Fraction of total variance explained limit for retaining factors using the variance limit criterion (where “n=varlimit”).
porig	Use the unreduced matrix for parallel analysis (the default is to use the reduced matrix). For parallel analysis only (“n=parallel”).
preps= integer (default=100)	Number of parallel analysis repetitions. For parallel analysis only (“n=parallel”).
pquant=number	Quantile value for parallel analysis comparison (if not specified, the mean value will be employed). For parallel analysis only (“n=parallel”).
pseed=positive integer	Seed the random number generator for parallel analysis. If not specified, EViews will seed the random number generator with a single integer draw from the default global random number generator. For parallel analysis only (“n=parallel”).
prnd=arg (default=“kn” or method previously set using rndseed)	Type of random number generator for the simulation: improved Knuth generator (“kn”), improved Mersenne Twister (“mt”), Knuth’s (1997) lagged Fibonacci generator used in EViews 4 (“kn4”) L’Ecuyer’s (1999) combined multiple recursive generator (“le”), Matsumoto and Nishimura’s (1998) Mersenne Twister used in EViews 4 (“mt4”). For parallel analysis only (“n=parallel”).
mfmethod=arg (default=“user”)	Maximum number of components used by selection methods: “schwert” (Schwert’s rule, default), “ah” (Ahn and Horenstein’s (2013) suggestion), “rootsize” (), “size” (), “user” (user specified value), where is the number of series and is the number of observations. (1) For use with all components retention methods apart from user-specified (“fsmethod=user”). (2) If setting “mfmethod=user”, you may specify the maximum number of components using “rmax=”. (3) Schwert’s rule sets the maximum number of components using the rule: let for and let ; then the default maximum lag is given by
rmax=arg (default=all)	User-specified maximum number of factors to retain (for use when “mfmethod=user”).
fsic=arg (default=avg)	Factor selection criterion (when “fsmethod=bn”): “icp1” (ICP1), “icp2” (ICP2), “icp3” (ICP3), “pcp1” (PCP1), “pcp2” (PCP1), “pcp3” (ICP3), “avg” (average of all criteria ICP1 through PCP3). Factor selection criterion (when “fsmethod=ah”): “er” (eigenvalue ratio), “gr” (growth ratio), “avg” (average of eigenvalue ratio and growth ratio). Factor selection criterion (when “fsmethod=simple”): “min” (minimum of: minimum eigenvalue, cumulative eigenvalue proportion, and maximum number of factors), “max” (maximum of: minimum eigenvalue, cumulative eigenvalue proportion, and maximum number of factors), “avg” (average the optimal number of factors as specified by the min and max rule, then round to the nearest integer).
demeantime	Demeans observations across time prior to component selection procedures, when “n=bn” or “n=ah”.
sdizetime	Standardizes observations across time prior to component selection procedures, when “n=bn” or “n=ah”.
demeancross	Demeans observations across cross-sections prior to component selection procedures, when “n=bn” or “n=ah”.
sdizecross	Standardizes observations across cross-sections prior to component selection procedures, when “n=bn” or “n=ah”.

Initial Communalities Options

priors=arg	Method for obtaining initial communalities: “smc” (squared multiple correlations), “max” (maximum absolute correlation”), “pace” (noniterative partitioned covariance estimation), “frac” (fraction of the diagonals of the original matrix; specified using “priorfrac=”), “random” (random fractions of the original diagonals), “user” (user-specified vector; specified using “priorunique”).
priorfrac=number	User-specified common fraction (between 0 and 1) to be used when “priors=frac”.
priorunique=arg	Vector of initial uniqueness estimates to be used when “priors=user”. By default, the values will be taken from the corresponding elements of the coefficient vector C.

Covariance Options

cov=arg (default=“cov”)	Covariance calculation method: ordinary (Pearson product moment) covariance (“cov”), ordinary correlation (“corr”), Spearman rank covariance (“rcov”), Spearman rank correlation (“rcorr”), Kendall’s tau-b (“taub”), Kendall’s tau-a (“taua”), uncentered ordinary covariance (“ucov”), uncentered ordinary correlation (“ucorr”). User-specified covariances are indicated by specifying a sym matrix object in place of a list of series or groups in the command.
wgt=name (optional)	Name of series containing weights.
wgtmethod=arg (default = “sstdev”)	Weighting method (when weights are specified using “weight=”): frequency (“freq”), inverse of variances (“var”), inverse of standard deviation (“stdev”), scaled inverse of variances (“svar”), scaled inverse of standard deviations (“sstdev”). Only applicable for ordinary (Pearson) calculations. Weights specified by “wgt=” are frequency weights for rank correlation and Kendall’s tau calculations.
pairwise	Compute using pairwise deletion of observations with missing cases (pairwise samples).
df	Compute covariances with a degree-of-freedom correction for the mean (for centered specifications), and any partial conditioning variables.

Examples

factor f1.gls(n=map, priors=max) group01

f1.gls(n=map, priors=max) group01 @partial ser1 ser2

estimates the same specification using the partial correlation for the series in GROUP01, conditional on the series SER1 and SER2.

f1.gls(rescale, maxit=200, n=2, priors=smc, cov=rcorr) x y z

estimates a two factor model for the rank correlation computed from the series X, Y, and Z, using generalized least squares with 200 maximum iterations. The result is rescaled if necessary so that estimated uniqueness and the communality sum to 1; the initial uniquenesses are set to the SMCs of the observed correlation matrix.

f1.gls sym01 393

estimates a factor model using the symmetric matrix object as the observed matrix. The number of observations for the model is set to 393.

Cross-references

See “Factor Analysis” for a general discussion of factor analysis. The various estimation methods are described in “Estimation Methods”.

See also Factor::ipf, Factor::ml, Factor::pace, Factor::pf, Factor::uls.

ipf	Factor Methods

Iterated principal factors estimation of the factor model.

Syntax

factor_name.ipf(options) x1 [x2 x3...] [@partial z1 z2 z3...]

factor_name.ipf(options) matrix_name [[obs] [conditioning]] [@ name1 name2 name3...]

The first method computes the observed dispersion matrix from a set of series or group objects. Simply append a period and the ipf keyword to the name of your object, followed by the names of your series and groups, You may optionally use the keyword @partial and append a list of conditioning series.

Options

Estimation Options

heywood=arg (default=“stop”)	Method for handling Heywood cases (negative uniqueness estimates): “stop” (stop and report final results), “last” (stop and report previous iteration results”, “reset” (set negative uniquenesses to zero and continue), “ignore” (ignore and continue).
maxit=integer	Maximum number of iterations.
conv=scalar	Set convergence criterion. The criterion is based upon the maximum of the percentage changes in the scaled estimates. The criterion will be set to the nearest value between 1e-24 and 0.2.
showopts / ‑showopts	[Do / do not] display the starting coefficient values and estimation options in the rotation output.
prompt	Force the dialog to appear from within a program.
p	Print basic estimation results.

Number of Factors Options

n=arg or fsmethod=arg (default=“map”)	Number of factors: “kaiser” (Kaiser-Guttman greater than mean), “mineigen” (Minimum eigenvalue criterion; specified using “eiglimit”), “varfrac” (fraction of variance accounted for; specified using “varlimit”), “map” (Velicer’s Minimum Average Partial method), “bstick” (comparison with broken stick distribution), “parallel” (parallel analysis: number of replications specified using “pnreps”; “pquant” indicates the quantile method value if employed), “scree” (standard error scree method), “bn” (Bai and Ng (2002)), “ah” (Ahn and Horenstein (2013)), integer (user-specified integer value).
eiglimit=number (default=1)	Limit value for retaining factors using the eigenvalue comparison (where “n=mineigen”).
varlimit=number (default=0.5)	Fraction of total variance explained limit for retaining factors using the variance limit criterion (where “n=varlimit”).
porig	Use the unreduced matrix for parallel analysis (the default is to use the reduced matrix). For parallel analysis only (“n=parallel”).
preps= integer (default=100)	Number of parallel analysis repetitions. For parallel analysis only (“n=parallel”).
pquant=number	Quantile value for parallel analysis comparison (if not specified, the mean value will be employed). For parallel analysis only (“n=parallel”).
pseed=positive integer	Seed the random number generator for parallel analysis. If not specified, EViews will seed the random number generator with a single integer draw from the default global random number generator. For parallel analysis only (“n=parallel”).
prnd=arg (default=“kn” or method previously set using rndseed)	Type of random number generator for the simulation: improved Knuth generator (“kn”), improved Mersenne Twister (“mt”), Knuth’s (1997) lagged Fibonacci generator used in EViews 4 (“kn4”) L’Ecuyer’s (1999) combined multiple recursive generator (“le”), Matsumoto and Nishimura’s (1998) Mersenne Twister used in EViews 4 (“mt4”). For parallel analysis only (“n=parallel”).
mfmethod=arg (default=“user”)	Maximum number of components used by selection methods: “schwert” (Schwert’s rule, default), “ah” (Ahn and Horenstein’s (2013) suggestion), “rootsize” (), “size” (), “user” (user specified value), where is the number of series and is the number of observations. (1) For use with all components retention methods apart from user-specified (“fsmethod=user”). (2) If setting “mfmethod=user”, you may specify the maximum number of components using “rmax=”. (3) Schwert’s rule sets the maximum number of components using the rule: let for and let ; then the default maximum lag is given by
rmax=arg (default=all)	User-specified maximum number of factors to retain (for use when “mfmethod=user”).
fsic=arg (default=avg)	Factor selection criterion (when “fsmethod=bn”): “icp1” (ICP1), “icp2” (ICP2), “icp3” (ICP3), “pcp1” (PCP1), “pcp2” (PCP1), “pcp3” (ICP3), “avg” (average of all criteria ICP1 through PCP3). Factor selection criterion (when “fsmethod=ah”): “er” (eigenvalue ratio), “gr” (growth ratio), “avg” (average of eigenvalue ratio and growth ratio). Factor selection criterion (when “fsmethod=simple”): “min” (minimum of: minimum eigenvalue, cumulative eigenvalue proportion, and maximum number of factors), “max” (maximum of: minimum eigenvalue, cumulative eigenvalue proportion, and maximum number of factors), “avg” (average the optimal number of factors as specified by the min and max rule, then round to the nearest integer).
demeantime	Demeans observations across time prior to component selection procedures, when “n=bn” or “n=ah”.
sdizetime	Standardizes observations across time prior to component selection procedures, when “n=bn” or “n=ah”.
demeancross	Demeans observations across cross-sections prior to component selection procedures, when “n=bn” or “n=ah”.
sdizecross	Standardizes observations across cross-sections prior to component selection procedures, when “n=bn” or “n=ah”.

Initial Communalities Options

priors=arg	Method for obtaining initial communalities: “smc” (squared multiple correlations), “max” (maximum absolute correlation”), “pace” (noniterative partitioned covariance estimation), “frac” (fraction of the diagonals of the original matrix; specified using “priorfrac=”), “random” (random fractions of the original diagonals), “user” (user-specified vector; specified using “priorunique”).
priorfrac=number	User-specified common fraction (between 0 and 1) to be used when “priors=frac”.
priorunique=arg	Vector of initial uniqueness estimates to be used when “priors=user”. By default, the values will be taken from the corresponding elements of the coefficient vector C.

Covariance Options

cov=arg (default=“cov”)	Covariance calculation method: ordinary (Pearson product moment) covariance (“cov”), ordinary correlation (“corr”), Spearman rank covariance (“rcov”), Spearman rank correlation (“rcorr”), Kendall’s tau-b (“taub”), Kendall’s tau-a (“taua”), uncentered ordinary covariance (“ucov”), uncentered ordinary correlation (“ucorr”). User-specified covariances are indicated by specifying a sym matrix object in place of a list of series or groups in the command.
wgt=name (optional)	Name of series containing weights.
wgtmethod=arg (default = “sstdev”)	Weighting method (when weights are specified using “weight=”): frequency (“freq”), inverse of variances (“var”), inverse of standard deviation (“stdev”), scaled inverse of variances (“svar”), scaled inverse of standard deviations (“sstdev”). Only applicable for ordinary (Pearson) calculations. Weights specified by “wgt=” are frequency weights for rank correlation and Kendall’s tau calculations.
pairwise	Compute using pairwise deletion of observations with missing cases (pairwise samples).
df	Compute covariances with a degree-of-freedom correction for the mean (for centered specifications), and any partial conditioning variables.

Examples

factor f1.ipf(n=2, maxit=4) var1 var2 var3 var4

declares the factor object F1 then extracts two factors from the variables VAR1–VAR4 by the iterative principal factor method, with a maximum of four iterations.

f1.ipf(conv=1e-9, heywood=reset) group01

sets the convergence criterion to 1e-9, and estimates the factor model for the series in GROUP01. If encountered, negative uniqueness estimates will be set to zero and the estimation will proceed.

f1.ipf(conv=1e-9, heywood=reset) group01 @partial ser1 ser2

estimates the same specification using the partial correlation for GROUP01, conditional on the series SER1 and SER2.

f1.ipf(n=parallel) sym01 424

estimates the iterative principal factor model using the observed matrix SYM01. The number of observations is 424, and the number of factors is determined using parallel analysis.

Cross-references

See “Factor Analysis” for a general discussion of factor analysis. The various estimation methods are described in “Estimation Methods”.

See also Factor::gls, Factor::ml, Factor::pace, Factor::pf, Factor::uls.

label

Factor Views | Factor Procs

Display or change the label view of the factor object.

Syntax

factor_name.label

factor_name.label(options) [text]

Options

The first version of the command displays the label view of the factor. The second version may be used to modify the label. Specify one of the following options along with optional text. If there is no text provided, the specified field will be cleared.

c	Clears all text fields in the label.
d	Sets the description field to text.
s	Sets the source field to text.
u	Sets the units field to text.
r	Appends text to the remarks field as an additional line.
p	Print the label view.

If no options are provided, label will display the current values in the label.

Examples

The following lines replace the remarks field of F1 with “Example factor analysis problem”:

f1.label(r) Example factor analysis problem

To append additional remarks to F1, and then to print the label view:

f1.label(r, p) Test evaluation

Cross-references

See “Labeling Objects” for a discussion of labels.

See also Factor::displayname.

loadings

Factor Views

Display factor loadings tables or graphs.

Syntax

factor_name.loadings(options)

factor_name.loadings(graph, options) [graph_list]

where the [graph_list] is an optional list of integers and/or vectors containing integers identifying the factors to plot. If graph_list is not provided, EViews will construct graphs using all of the retained factors.

Multiple pairs are handled using the method specified in the “mult=” option. Note that the order of elements in the list matters; reversing the order of two indices reverses the axis on which each factor is displayed.

Options

graph	Display graphs of the loadings (default is to display the loadings in a spreadsheet view).
unrotated	Use the unrotated loadings (default is to use the rotated loadings, if available).
prompt	Force the dialog to appear from within a program (for loadings graphs only)
p	Print results.

Graph Options

mult =arg (default=“first”)	Multiple series handling: plot first against remainder (“first”), plot as x-y pairs (“pair”), lower-triangular plot (“lt”).
nocenter	Do not center graphs around the origin. By default, EViews centers biplots around (0, 0).

Examples

f1.loadings

displays the spreadsheet view of the (possibly rotated) loadings.

f1.loadings(graph, unrotated) 1 2

displays an XY graph of the first two unrotated factor loadings.

Cross-references

See “Background” for a general discussion of the factor model, and “Loadings Views” for specific discussion of the loadings view.

makescores

Factor Procs

Save estimated factor score series in the workfile

Syntax

factor_name.makescores(options) [output_list] [@ observed_list]

The optional output_list describes the factors that you wish to save. There are two formats for the list:

• You may specify output_list using a list of integers and/or vectors containing integers identifying the factors that you wish to save (e.g., “1 2 3 5”).

EViews will construct the output series names using the factor names previously specified in the factor object (using Factor::factnames) or using the default names “F1”, “F2”, etc. If a name modifier is provided (using the “append=” option), it will be appended to each name

• You may provide an output_list containing names for factors to be saved (e.g., “math science verbal”).

If you provide

factor names, EViews will save the first

factors to the workfile. The factors will be named using the specified list, appended with the name modifiers, if specified.

By default, EViews will save all of the factors using the names in the factor object, with modifiers if necessary.

The optional observed_list of observed input variables will be multiplied by the score coefficients to compute the scores. Note that:

• If an observed_list is not provided, EViews will use the observed variables from factor estimation. For user-specified factor models (specified by providing a symmetric matrix) you must provide a list if you wish to obtain score values.

• Scores values will be computed for the current workfile sample. Observations with input values that are missing will generate NAs.

Options

unrotated	Use unrotated loadings in computations (the default is to use the rotated loadings, if available).
type =arg (default=“exact”)	Exact coefficient (“exact”), coarse adjusted factor coefficients (“coefs”), coarse adjusted factor loadings (“loadings”).
coef=arg (default=“reg”)	Method for computing the factor score coefficient matrix: Thurstone regression (“reg”), Ideal Variables (“ideal”), Bartlett weighted least squares (“wls”), generalized Anderson-Rubin-McDonald (“anderson”), Green (“green”). For “type=exact” and “type=coefs” specifications.
coarse=arg (default=“unrestrict”)	Method for computing the coarse (-1, 0, 1) scores coefficients (Grice, 1991a): Unrestricted -- (“unrestrict”) coef weights set based only on sign; Unique–recode (“recode”) only element with highest value is coded to a non-zero value; Unique–drop (“drop”) only elements with loadings not in excess of the threshold are set to non-zero values. For “type=coefs” and “type=loadings” specifications.
cutoff=number (default = 0.3)	Cutoff value for coarse score coefficient calculation (Grice, 1991a). For “type=coef” specifications, the cutoff value represents the fraction of the largest absolute coefficient weight per factor against which the absolute exact score coefficients should be compared. For “type=loadings”, and “type=struct” specifications, the cutoff is the value against which the absolute loadings or structure coefficients should be compared.
moment=arg (default =“est”; if feasible)	Standardize the observables data using means and variances from: original estimation (“est”), or the computed moments from specified observable variables (“obs”). The “moment=est” option is only available for factor models estimated using Pearson or uncentered Pearson correlation and covariances since the remaining models involve unobserved or non-comparable moments.
df	Degrees-of-freedom correct the observables variances computed when “moment=obs” (divide sums-of-squares by instead of ).
n=arg	(Optional) Name of group object to contain the factor score series.
coefout	(Optional) Name of matrix in which to save the factor score coefficient matrix.
prompt	Force the dialog to appear from within a program.

Examples

f1.makescores(coef=green, n=outgrp)

computes factor scores coefficients using Green’s method, then saves the results into series in the workfile using the names in the factor object. The observed data from the estimation specification will be used as inputs to the procedure. If no names have been specified, the names will be “F1”, “F2”, etc. The output series will be saved in the group object OUTGRP.

f1.makescores(coef=green, n=outgrp) 1 2

computes scores in the same fashion, but only saves factors 1 and 2.

f1.makescores(type=coefs) sc1 sc2 sc3

computes coarse factor scores using the default (Thurstone) scores coefficients and saves them in the series SC1, SC2, and SC3. The observed data from the estimation specification will be used as inputs.

Cross-references

See “Estimating Scores”and “Scoring”. See also Factor::scores.

maxcor

Factor Views

Display the maximum absolute correlations for each column of the observed covariance matrix.

Syntax

factor_name.maxcor(options)

The table also displays the observed covariance matrix.

Options

p	Print the matrix.

Examples

f1.maxcor(p)

displays and prints the maximum absolute covariance matrix for the factor object F1.

Cross-references

See also Factor::anticov, Factor::observed, and Factor::partcor.

ml	Factor Methods

Maximum likelihood estimation of the factor model.

Syntax

factor_name.ml(options) x1 [x2 x3...] [@partial z1 z2 z3...]

factor_name.ml(options) matrix_name [[obs] [conditioning]] [@ name1 name2 name3...]

The first method computes the observed dispersion matrix from a set of series or group objects. Simply append a period and the ml keyword to the name of your object, followed by the names of your series and groups, You may optionally use the keyword @partial and append a list of conditioning series.

Options

Estimation Options

rescale	Rescale the uniqueness and loadings estimates so that they match the observed variances.
maxit=integer	Maximum number of iterations.
conv=scalar	Set convergence criterion. The criterion is based upon the maximum of the percentage changes in the scaled estimates. The criterion will be set to the nearest value between 1e-24 and 0.2.
showopts / ‑showopts	[Do / do not] display the starting coefficient values and estimation options in the rotation output.
prompt	Force the dialog to appear from within a program.
p	Print basic estimation results.

Number of Factors Options

n=arg or fsmethod=arg (default=“map”)	Number of factors: “kaiser” (Kaiser-Guttman greater than mean), “mineigen” (Minimum eigenvalue criterion; specified using “eiglimit”), “varfrac” (fraction of variance accounted for; specified using “varlimit”), “map” (Velicer’s Minimum Average Partial method), “bstick” (comparison with broken stick distribution), “parallel” (parallel analysis: number of replications specified using “pnreps”; “pquant” indicates the quantile method value if employed), “scree” (standard error scree method), “bn” (Bai and Ng (2002)), “ah” (Ahn and Horenstein (2013)), integer (user-specified integer value).
eiglimit=number (default=1)	Limit value for retaining factors using the eigenvalue comparison (where “n=mineigen”).
varlimit=number (default=0.5)	Fraction of total variance explained limit for retaining factors using the variance limit criterion (where “n=varlimit”).
porig	Use the unreduced matrix for parallel analysis (the default is to use the reduced matrix). For parallel analysis only (“n=parallel”).
preps= integer (default=100)	Number of parallel analysis repetitions. For parallel analysis only (“n=parallel”).
pquant=number	Quantile value for parallel analysis comparison (if not specified, the mean value will be employed). For parallel analysis only (“n=parallel”).
pseed=positive integer	Seed the random number generator for parallel analysis. If not specified, EViews will seed the random number generator with a single integer draw from the default global random number generator. For parallel analysis only (“n=parallel”).
prnd=arg (default=“kn” or method previously set using rndseed)	Type of random number generator for the simulation: improved Knuth generator (“kn”), improved Mersenne Twister (“mt”), Knuth’s (1997) lagged Fibonacci generator used in EViews 4 (“kn4”) L’Ecuyer’s (1999) combined multiple recursive generator (“le”), Matsumoto and Nishimura’s (1998) Mersenne Twister used in EViews 4 (“mt4”). For parallel analysis only (“n=parallel”).
mfmethod=arg (default=“user”)	Maximum number of components used by selection methods: “schwert” (Schwert’s rule, default), “ah” (Ahn and Horenstein’s (2013) suggestion), “rootsize” (), “size” (), “user” (user specified value), where is the number of series and is the number of observations. (1) For use with all components retention methods apart from user-specified (“fsmethod=user”). (2) If setting “mfmethod=user”, you may specify the maximum number of components using “rmax=”. (3) Schwert’s rule sets the maximum number of components using the rule: let for and let ; then the default maximum lag is given by
rmax=arg (default=all)	User-specified maximum number of factors to retain (for use when “mfmethod=user”).
fsic=arg (default=avg)	Factor selection criterion (when “fsmethod=bn”): “icp1” (ICP1), “icp2” (ICP2), “icp3” (ICP3), “pcp1” (PCP1), “pcp2” (PCP1), “pcp3” (ICP3), “avg” (average of all criteria ICP1 through PCP3). Factor selection criterion (when “fsmethod=ah”): “er” (eigenvalue ratio), “gr” (growth ratio), “avg” (average of eigenvalue ratio and growth ratio). Factor selection criterion (when “fsmethod=simple”): “min” (minimum of: minimum eigenvalue, cumulative eigenvalue proportion, and maximum number of factors), “max” (maximum of: minimum eigenvalue, cumulative eigenvalue proportion, and maximum number of factors), “avg” (average the optimal number of factors as specified by the min and max rule, then round to the nearest integer).
demeantime	Demeans observations across time prior to component selection procedures, when “n=bn” or “n=ah”.
sdizetime	Standardizes observations across time prior to component selection procedures, when “n=bn” or “n=ah”.
demeancross	Demeans observations across cross-sections prior to component selection procedures, when “n=bn” or “n=ah”.
sdizecross	Standardizes observations across cross-sections prior to component selection procedures, when “n=bn” or “n=ah”.

Initial Communalities Options

priors=arg	Method for obtaining initial communalities: “smc” (squared multiple correlations), “max” (maximum absolute correlation”), “pace” (noniterative partitioned covariance estimation), “frac” (fraction of the diagonals of the original matrix; specified using “priorfrac=”), “random” (random fractions of the original diagonals), “user” (user-specified vector; specified using “priorunique”).
priorfrac=number	User-specified common fraction (between 0 and 1) to be used when “priors=frac”.
priorunique=arg	Vector of initial uniqueness estimates to be used when “priors=user”. By default, the values will be taken from the corresponding elements of the coefficient vector C.

Covariance Options

cov=arg (default=“cov”)	Covariance calculation method: ordinary (Pearson product moment) covariance (“cov”), ordinary correlation (“corr”), Spearman rank covariance (“rcov”), Spearman rank correlation (“rcorr”), Kendall’s tau-b (“taub”), Kendall’s tau-a (“taua”), uncentered ordinary covariance (“ucov”), uncentered ordinary correlation (“ucorr”). User-specified covariances are indicated by specifying a sym matrix object in place of a list of series or groups in the command.
wgt=name (optional)	Name of series containing weights.
wgtmethod=arg (default = “sstdev”)	Weighting method (when weights are specified using “weight=”): frequency (“freq”), inverse of variances (“var”), inverse of standard deviation (“stdev”), scaled inverse of variances (“svar”), scaled inverse of standard deviations (“sstdev”). Only applicable for ordinary (Pearson) calculations. Weights specified by “wgt=” are frequency weights for rank correlation and Kendall’s tau calculations.
pairwise	Compute using pairwise deletion of observations with missing cases (pairwise samples).
df	Compute covariances with a degree-of-freedom correction for the mean (for centered specifications), and any partial conditioning variables.

Examples

factor f1.ml group01

declares the factor object F1 then estimates the factor model using the correlation matrix for the series in GROUP01 by the method of maximum likelihood.

f1.ml group01 @partial ser1 ser2

estimates the same specification using the partial correlation for the series in GROUP01, conditional on the series SER1 and SER2.

f1.ml(n=parallel, priors=max) x y z

uses parallel analysis to determine the number of factors for a model estimates from the series X, Y, and Z, and uses the maximum absolute correlations to determine the initial uniqueness estimates.

f1.ml(n=scree) sym01 424

estimates the factor model using the observed matrix SYM01. The number of observations is 424, and the number of factors is determined using the standard error scree.

Cross-references

See “Factor Analysis” for a general discussion of factor analysis. The various estimation methods are described in “Estimation Methods”.

See also Factor::gls, Factor::ipf, Factor::ml, Factor::pace, Factor::pf, Factor::uls.

msa	Factor Views

Display Kaiser’s Measure of Sampling Adequacy and matrix of partial correlations.

Syntax

factor_name.msa(options)

Options

p	Print the results.

Examples

f1.msa(p)

displays and prints the results for the factor object F1.

Cross-references

See “Basic Diagnostic Views” for discussion.

See also Factor::partcor and Factor::anticov.

observed

Factor Views

Display observed covariance matrix, scaled observed covariance (correlation), or matrix of number of observations.

Syntax

factor_name.observed(options)

Options

scaled	Scale the observed matrix so that it has unit diagonals.
p	Print the results.

Examples

factor f1.ml group01

f1.observed

estimates a common factor model for the series in GROUP01, then displays the observed covariance matrix.

f1.observed(scaled, p)

displays and prints the corresponding correlation matrix.

Cross-references

See “Observed Covariances” .

See also Factor::anticov, Factor::partcor, and Factor::smc.

olepush

Factor Procs

Push updates to OLE linked objects in open applications.

Syntax

factor_name.olepush

Cross-references

See “Object Linking and Embedding (OLE)” for a discussion of using OLE with EViews.

output

Factor Views

Display factor estimation output.

Syntax

factor_name.output(options)

Options

p	Print view.

Examples

f1.output

displays the estimation output for factor F1.

Cross-references

See “Factor Analysis” for a general discussion of factor analysis. The various estimation methods are described in “Estimation Methods”.

pace	Factor Methods

Non-iterative partitioned covariance estimation of the factor model

Syntax

factor_name.pace(options) x1 [x2 x3...] [@partial z1 z2 z3...]

factor_name.pace(options) matrix_name [[obs] [conditioning]] [@ name1 name2 name3...]

The first method computes the observed dispersion matrix from a set of series or group objects. Simply append a period and the pace keyword to the name of your object, followed by the names of your series and groups, You may optionally use the keyword @partial and append a list of conditioning series.

Options

Estimation Options

rescale	Rescale the uniqueness and loadings estimates so that they match the observed variances.
prompt	Force the dialog to appear from within a program.
p	Print basic estimation results.

Number of Factors Options

n=arg or fsmethod=arg (default=“map”)	Number of factors: “kaiser” (Kaiser-Guttman greater than mean), “mineigen” (Minimum eigenvalue criterion; specified using “eiglimit”), “varfrac” (fraction of variance accounted for; specified using “varlimit”), “map” (Velicer’s Minimum Average Partial method), “bstick” (comparison with broken stick distribution), “parallel” (parallel analysis: number of replications specified using “pnreps”; “pquant” indicates the quantile method value if employed), “scree” (standard error scree method), “bn” (Bai and Ng (2002)), “ah” (Ahn and Horenstein (2013)), integer (user-specified integer value).
eiglimit=number (default=1)	Limit value for retaining factors using the eigenvalue comparison (where “n=mineigen”).
varlimit=number (default=0.5)	Fraction of total variance explained limit for retaining factors using the variance limit criterion (where “n=varlimit”).
porig	Use the unreduced matrix for parallel analysis (the default is to use the reduced matrix). For parallel analysis only (“n=parallel”).
preps= integer (default=100)	Number of parallel analysis repetitions. For parallel analysis only (“n=parallel”).
pquant=number	Quantile value for parallel analysis comparison (if not specified, the mean value will be employed). For parallel analysis only (“n=parallel”).
pseed=positive integer	Seed the random number generator for parallel analysis. If not specified, EViews will seed the random number generator with a single integer draw from the default global random number generator. For parallel analysis only (“n=parallel”).
prnd=arg (default=“kn” or method previously set using rndseed)	Type of random number generator for the simulation: improved Knuth generator (“kn”), improved Mersenne Twister (“mt”), Knuth’s (1997) lagged Fibonacci generator used in EViews 4 (“kn4”) L’Ecuyer’s (1999) combined multiple recursive generator (“le”), Matsumoto and Nishimura’s (1998) Mersenne Twister used in EViews 4 (“mt4”). For parallel analysis only (“n=parallel”).
mfmethod=arg (default=“user”)	Maximum number of components used by selection methods: “schwert” (Schwert’s rule, default), “ah” (Ahn and Horenstein’s (2013) suggestion), “rootsize” (), “size” (), “user” (user specified value), where is the number of series and is the number of observations. (1) For use with all components retention methods apart from user-specified (“fsmethod=user”). (2) If setting “mfmethod=user”, you may specify the maximum number of components using “rmax=”. (3) Schwert’s rule sets the maximum number of components using the rule: let for and let ; then the default maximum lag is given by
rmax=arg (default=all)	User-specified maximum number of factors to retain (for use when “mfmethod=user”).
fsic=arg (default=avg)	Factor selection criterion (when “fsmethod=bn”): “icp1” (ICP1), “icp2” (ICP2), “icp3” (ICP3), “pcp1” (PCP1), “pcp2” (PCP1), “pcp3” (ICP3), “avg” (average of all criteria ICP1 through PCP3). Factor selection criterion (when “fsmethod=ah”): “er” (eigenvalue ratio), “gr” (growth ratio), “avg” (average of eigenvalue ratio and growth ratio). Factor selection criterion (when “fsmethod=simple”): “min” (minimum of: minimum eigenvalue, cumulative eigenvalue proportion, and maximum number of factors), “max” (maximum of: minimum eigenvalue, cumulative eigenvalue proportion, and maximum number of factors), “avg” (average the optimal number of factors as specified by the min and max rule, then round to the nearest integer).
demeantime	Demeans observations across time prior to component selection procedures, when “n=bn” or “n=ah”.
sdizetime	Standardizes observations across time prior to component selection procedures, when “n=bn” or “n=ah”.
demeancross	Demeans observations across cross-sections prior to component selection procedures, when “n=bn” or “n=ah”.
sdizecross	Standardizes observations across cross-sections prior to component selection procedures, when “n=bn” or “n=ah”.

Covariance Options

cov=arg (default=“cov”)	Covariance calculation method: ordinary (Pearson product moment) covariance (“cov”), ordinary correlation (“corr”), Spearman rank covariance (“rcov”), Spearman rank correlation (“rcorr”), Kendall’s tau-b (“taub”), Kendall’s tau-a (“taua”), uncentered ordinary covariance (“ucov”), uncentered ordinary correlation (“ucorr”). User-specified covariances are indicated by specifying a sym matrix object in place of a list of series or groups in the command.
wgt=name (optional)	Name of series containing weights.
wgtmethod=arg (default = “sstdev”)	Weighting method (when weights are specified using “weight=”): frequency (“freq”), inverse of variances (“var”), inverse of standard deviation (“stdev”), scaled inverse of variances (“svar”), scaled inverse of standard deviations (“sstdev”). Only applicable for ordinary (Pearson) calculations. Weights specified by “wgt=” are frequency weights for rank correlation and Kendall’s tau calculations.
pairwise	Compute using pairwise deletion of observations with missing cases (pairwise samples).
df	Compute covariances with a degree-of-freedom correction for the mean (for centered specifications), and any partial conditioning variables.

Examples

factor f1.pace(n=map, rescale) x y z

declares the factor object F1 and estimates the factors for the correlation matrix of X, Y, and Z, by the PACE method. The number of factors is determined by Velicer’s MAP procedure and the result is rescaled to match the observed variances.

f1.pace(n=3) group01

estimates the three factor model for the series in GROUP01 by the PACE method.

f1.pace(n=3) group01 @partial ser1 ser2

estimates the same specification using the partial correlation for the series in GROUP01, conditional on the series SER1 and SER2.

f1.pace(n=scree) sym01 848

estimates the PACE factor model using the observed matrix SYM01. The number of observations is 848, and the number of factors is determined using the standard error scree.

Cross-references

See “Factor Analysis” for a general discussion of factor analysis. The various estimation methods are described in “Estimation Methods”.

See also Factor::gls, Factor::ipf, Factor::ml, Factor::pf, Factor::uls.

partcor

Factor Views

Display the partial correlation matrix derived from the observed covariance matrix.

Syntax

factor_name.partcor(options)

The elements of the partial correlation matrix are the pairwise correlations conditional on the other variables.

The partial correlation matrix is computed by scaling the anti-image covariance to unit diagonal (or equivalently, by row and column scaling the inverse of the observed matrix by the square roots of its diagonals).

Options

p	Print the matrix.

Examples

factor f1.ml group01

f1.partcor(p)

displays and prints the partial correlation matrix for the factor object F1.

Cross-references

See “Observed Covariances”.

See also Factor::anticov, Factor::observed, and Factor::smc.

pf	Factor Methods

Principal factors estimation of the factor model.

Syntax

factor_name.pf(options) x1 [x2 x3...] [@partial z1 z2 z3...]

factor_name.pf(options) matrix_name [[obs] [conditioning]] [@ name1 name2 name3...]

The first method computes the observed dispersion matrix from a set of series or group objects. Simply append a period and the pf keyword to the name of your object, followed by the names of your series and groups, You may optionally use the keyword @partial and append a list of conditioning series.

Options

Estimation Options

prompt	Force the dialog to appear from within a program.
p	Print basic estimation results.

Number of Factors Options

n=arg or fsmethod=arg (default=“map”)	Number of factors: “kaiser” (Kaiser-Guttman greater than mean), “mineigen” (Minimum eigenvalue criterion; specified using “eiglimit”), “varfrac” (fraction of variance accounted for; specified using “varlimit”), “map” (Velicer’s Minimum Average Partial method), “bstick” (comparison with broken stick distribution), “parallel” (parallel analysis: number of replications specified using “pnreps”; “pquant” indicates the quantile method value if employed), “scree” (standard error scree method), “bn” (Bai and Ng (2002)), “ah” (Ahn and Horenstein (2013)), integer (user-specified integer value).
eiglimit=number (default=1)	Limit value for retaining factors using the eigenvalue comparison (where “n=mineigen”).
varlimit=number (default=0.5)	Fraction of total variance explained limit for retaining factors using the variance limit criterion (where “n=varlimit”).
porig	Use the unreduced matrix for parallel analysis (the default is to use the reduced matrix). For parallel analysis only (“n=parallel”).
preps= integer (default=100)	Number of parallel analysis repetitions. For parallel analysis only (“n=parallel”).
pquant=number	Quantile value for parallel analysis comparison (if not specified, the mean value will be employed). For parallel analysis only (“n=parallel”).
pseed=positive integer	Seed the random number generator for parallel analysis. If not specified, EViews will seed the random number generator with a single integer draw from the default global random number generator. For parallel analysis only (“n=parallel”).
prnd=arg (default=“kn” or method previously set using rndseed)	Type of random number generator for the simulation: improved Knuth generator (“kn”), improved Mersenne Twister (“mt”), Knuth’s (1997) lagged Fibonacci generator used in EViews 4 (“kn4”) L’Ecuyer’s (1999) combined multiple recursive generator (“le”), Matsumoto and Nishimura’s (1998) Mersenne Twister used in EViews 4 (“mt4”). For parallel analysis only (“n=parallel”).
mfmethod=arg (default=“user”)	Maximum number of components used by selection methods: “schwert” (Schwert’s rule, default), “ah” (Ahn and Horenstein’s (2013) suggestion), “rootsize” (), “size” (), “user” (user specified value), where is the number of series and is the number of observations. (1) For use with all components retention methods apart from user-specified (“fsmethod=user”). (2) If setting “mfmethod=user”, you may specify the maximum number of components using “rmax=”. (3) Schwert’s rule sets the maximum number of components using the rule: let for and let ; then the default maximum lag is given by
rmax=arg (default=all)	User-specified maximum number of factors to retain (for use when “mfmethod=user”).
fsic=arg (default=avg)	Factor selection criterion (when “fsmethod=bn”): “icp1” (ICP1), “icp2” (ICP2), “icp3” (ICP3), “pcp1” (PCP1), “pcp2” (PCP1), “pcp3” (ICP3), “avg” (average of all criteria ICP1 through PCP3). Factor selection criterion (when “fsmethod=ah”): “er” (eigenvalue ratio), “gr” (growth ratio), “avg” (average of eigenvalue ratio and growth ratio). Factor selection criterion (when “fsmethod=simple”): “min” (minimum of: minimum eigenvalue, cumulative eigenvalue proportion, and maximum number of factors), “max” (maximum of: minimum eigenvalue, cumulative eigenvalue proportion, and maximum number of factors), “avg” (average the optimal number of factors as specified by the min and max rule, then round to the nearest integer).
demeantime	Demeans observations across time prior to component selection procedures, when “n=bn” or “n=ah”.
sdizetime	Standardizes observations across time prior to component selection procedures, when “n=bn” or “n=ah”.
demeancross	Demeans observations across cross-sections prior to component selection procedures, when “n=bn” or “n=ah”.
sdizecross	Standardizes observations across cross-sections prior to component selection procedures, when “n=bn” or “n=ah”.

Initial Communalities Options

priors=arg	Method for obtaining initial communalities: “smc” (squared multiple correlations), “max” (maximum absolute correlation”), “pace” (noniterative partitioned covariance estimation), “frac” (fraction of the diagonals of the original matrix; specified using “priorfrac=”), “random” (random fractions of the original diagonals), “user” (user-specified vector; specified using “priorunique”).
priorfrac=number	User-specified common fraction (between 0 and 1) to be used when “priors=frac”.
priorunique=arg	Vector of initial uniqueness estimates to be used when “priors=user”. By default, the values will be taken from the corresponding elements of the coefficient vector C.

Covariance Options

cov=arg (default=“cov”)	Covariance calculation method: ordinary (Pearson product moment) covariance (“cov”), ordinary correlation (“corr”), Spearman rank covariance (“rcov”), Spearman rank correlation (“rcorr”), Kendall’s tau-b (“taub”), Kendall’s tau-a (“taua”), uncentered ordinary covariance (“ucov”), uncentered ordinary correlation (“ucorr”). User-specified covariances are indicated by specifying a sym matrix object in place of a list of series or groups in the command.
wgt=name (optional)	Name of series containing weights.
wgtmethod=arg (default = “sstdev”)	Weighting method (when weights are specified using “weight=”): frequency (“freq”), inverse of variances (“var”), inverse of standard deviation (“stdev”), scaled inverse of variances (“svar”), scaled inverse of standard deviations (“sstdev”). Only applicable for ordinary (Pearson) calculations. Weights specified by “wgt=” are frequency weights for rank correlation and Kendall’s tau calculations.
pairwise	Compute using pairwise deletion of observations with missing cases (pairwise samples).
df	Compute covariances with a degree-of-freedom correction for the mean (for centered specifications), and any partial conditioning variables.

Examples

factor f1.pf(n=map, priors=frac, priorfrac=1) x y z

declares the factor object F1 and extracts factors from the correlation matrix of the series X, Y, and Z, by the principal factor method. The original variances are used as the initial uniqueness estimates.

f1.pf(priors=pace) group01

extracts factors for the correlation of the series in GROUP01 by the principal factor method with initial uniqueness estimated by the PACE method.

f1.pf(priors=pace) group01 @partial ser1 ser2

estimates the same specification using the partial correlation for the series in GROUP01, conditional on the series SER1 and SER2.

Cross-references

See “Factor Analysis” for a general discussion of factor analysis. The various estimation methods are described in “Estimation Methods”. See also Factor::gls, Factor::ipf, Factor::ml, Factor::pace, Factor::uls.

reduced

Factor Views

Display reduced covariance matrix for the estimated factor analysis object.

Syntax

factor_name.reduced(options)

By default, the reduced covariance is computed by subtracting the final uniqueness estimates from the observed covariance matrix. You may use the “initial” option to evaluate the reduced matrix using the initial uniqueness estimates.

Options

initial	Display the reduced matrix computed using the initial uniqueness estimates.
p	Print the matrix.

Examples

factor f1.pf x1 x2 x3 x4 x5 x6 x7 x8

f1.reduced

estimates a factor analysis model applied to the series X1 to X8 and displays the final reduced matrix (using final uniqueness estimates).

f1.reduced(initial)

displays the reduced matrix with the initial uniquenesses on the diagonal.

Cross-references

See “Matrix Views”.

type=arg (default=“orthog”)	Orthogonal (“orthog”) or oblique (“oblique”) rotation (ignored if method is not supported, e.g, “orthogonal Harris-Kaiser” or “oblique Entropy Ratio”).
method=arg (default=“varimax”)	Method (objective) for the rotation. See keywords below
param=arg	Rotation parameter, if applicable (see description below).
preparam=arg (default=1, Varimax)	Orthomax pre-rotation parameter (for “method=hk” and “method=promax”).

Method	Keyword	Orthogonal	Oblique
Biquartimax	biquartimax	•	•
Crawford-Ferguson	cf	•	•
Entropy	entropy	•
Entropy Ratio	entratio	•
Equamax	equamax	•	•
Factor Parsimony	parsimony	•	•
Generalized Crawford-Ferguson	gcf	•	•
Geomin	geomin	•	•
Harris-Kaiser (case II)	hk		•
Infomax	infomax	•	•
Oblimax	oblimax		•
Oblimin	oblimin		•
Orthomax	orthomax	•	•
Parsimax	parsimax	•	•
Pattern Simplicity	pattern	•	•
Promax	promax		•
Quartimax/Quartimin	quartimax	•	•
Simplimax	simplimax	•	•
Tandem I	tandemi	•
Tandem II	tandemii	•
Target	target	•	•
Varimax	varimax	•	•

Method		Parameter Description
Crawford-Ferguson	1	Factor complexity weight. The variable complexity weight is 1 minus the factor complexity weight. (default=0, Quartimax)
Generalized Crawford-Ferguson	4	Vector of weights for (in order): total squares, variable complexity, factor complexity, diagonal quartics. (no default)
Geomin	1	Epsilon offset. (default=0.01)
Harris-Kaiser (case II)	2	Power parameter (default=0, independent cluster solution), Orthomax pre-rotation parameter. (default=1, Varimax)
Oblimin	1	Deviation from orthogonality. (default=0, Quartimin)
Orthomax	1	Factor complexity weight. (default=1, Varimax)
Promax	2	Power parameter (default=3), Orthomax pre-rotation parameter (default=1, Varimax).
Simplimax	1	Fraction of near-zero loadings. (default=0.75)
Target	1	Name of matrix of target loadings. Missing values correspond to unrestricted elements. (no default)

wgts=arg (default=“none”)	Row weighting for loadings: none (“none”), kaiser (“kaiser”), Cureton-Mulaik (“cureton”).
prior=arg (default =“unrotated”)	Initial rotation matrix: unrotated (“unrotated”), randomly generated (“random”), previous rotation (“previous”), user-specified (“user”).
ptype=arg (default=“orthog”)	Type of prior random rotation: orthogonal (“orthog”) or oblique (“oblique”). Only relevant if “prior=random” and the main rotation method is oblique. If the main rotation method is orthogonal, random prior rotations will be orthogonalized.
preps=integer (default=25)	Number of random prior rotations to evaluate (maximum 10000).
pname=arg	Name of matrix containing prior rotation.
pseed=positive integer	Seed the random number generator for the prior random rotations. If not specified, EViews will seed the random number generator with a single integer draw from the default global random number generator.
prnd=arg (default=“kn” or method previously set using rndseed)	Type of random number generator for the random prior rotation: improved Knuth generator (“kn”), improved Mersenne Twister (“mt”), Knuth’s (1997) lagged Fibonacci generator used in EViews 4 (“kn4”) L’Ecuyer’s (1999) combined multiple recursive generator (“le”), Matsumoto and Nishimura’s (1998) Mersenne Twister used in EViews 4 (“mt4”).
m=integer	Maximum number of iterations.
c=scalar	Set convergence criterion. The criterion is based upon the norm of the gradients scaled by the objective function. The criterion will be set to the nearest value between 1e-24 and 0.2.
showopts / ‑showopts	[Do / do not] display the starting coefficient values and estimation options in the rotation output.
p	Print rotation results.

mult =arg (default=“first”)	Multiple series handling for graphs: plot first against remainder (“first”), plot as x-y pairs (“pair”), lower-triangular plot (“lt”)
nocenter	Do not center graphs around the origin.
labels=arg, (default=“outlier”)	Observation labels for scores: outliers only (“outlier”), all points (“all”), none (“none”).
labelprob=number	Probability value for determining whether a point is an outlier according to the chi-square tests based on the squared Mahalanbois distance between the observation and the sample means (when using the “labels=outlier” option).
userscale=arg	User-scale factor to be applied to the unscaled loadings (setting this option overrides the automatic scaling).
autoscale=arg (default = 1)	User-scale factor to be applied to the automatic loadings scale (when displaying both loadings and scores).

common	Display the residuals computed using only the common fitted covariance.
p	Print the matrix.

out=arg (default=“table”)	Output format: coefficient summary and diagnostics (“table”), spreadsheet table of scores (“sheet”), graph of scores (“graph”), graph of scores with loadings axes (“biplot”).
unrotated	Use unrotated loadings in computations (the default is to use the rotated loadings, if available).
type =arg (default=“exact”)	Exact coefficient (“exact”), coarse adjusted factor coefficients (“coefs”), coarse adjusted factor loadings (“loadings”).
coef=arg (default=“reg”)	Method for computing the exact or coarse adjusted factor score coefficient matrix: Thurstone regression (“reg”), Ideal Variables (“ideal”), Bartlett weighted least squares (“wls”), generalized Anderson-Rubin-McDonald (“anderson”), Green (“green”). For “type=exact” and “type=coefs” specifications.
coarse=arg (default=“unrestrict”)	Method for computing the coarse (-1, 0, 1) scores coefficients (Grice, 1991a): Unrestricted -- (“unrestrict”) coef weights set based only on sign; Unique–recode (“recode”) only element with highest value is coded to a non-zero value; Unique–drop (“drop”) only elements with loadings not in excess of the threshold are set to non-zero values. For “type=coefs” and “type=loadings” specifications.
cutoff=number (default = 0.3)	Cutoff value for coarse scores coefficient calculations (Grice, 1991a). For “type=coefs” specifications, the cutoff value represents the fraction of the largest absolute coefficient weight per factor against which the exact score coefficients should be compared. For “type=loadings” specifications, the cutoff is the value against which the absolute loadings or structure coefficients should be compared.
moment=arg (default =“est”; if feasible)	Standardize the observables data using means and variances from: original estimation (“est”), the computed moments from specified observable variables (“obs”). The “moment=est” option is only available for factor models estimated using Pearson or uncentered Pearson correlation and covariances since the remaining models involve unobserved or non-comparable moments.
df	Degrees-of-freedom correct the observables variances computed when “moment=obs” (divide sums-of-squares by instead of ).
coefout	(Optional) Name of matrix in which to save factor score coefficient matrix.
prompt	Force the dialog to appear from within a program.
p	Print results.