sem (version 0.8-0)

mod.indices: Modification Indices for Structural Equation Models

Description

mod.indices calculates modification indices (score tests) and estimated parameter changes for the fixed and constrained parameters in a structural equation model. [Warning: This is a preliminary version: the computed values are a bit off the correct values.]

Usage

mod.indices(model, ...)

## S3 method for class 'sem':
mod.indices(model, ...)

## S3 method for class 'sem.modind':
print(x, n.largest=5, ...)

## S3 method for class 'sem.modind':
summary(object, round=2, 
    print.matrices=c("both", "par.change", "mod.indices"), ...)

Arguments

model

an object of class sem, produced by the sem function.

object, x

an object of class sem.modind, produced by the mod.indices function.

n.largest

number of modification indices to print in each of the eqn{A} and eqn{P} matrices of the RAM model.

round

number of places to the right of the decimal point in printing modification indices.

print.matrices

which matrices to print: estimated changes in the fixed parameters, modification indices, or both (the default).

...

arguments to be passed down.

Value

• mod.indices returns an object of class sem.modind with the following elements:
• mod.A
  modification indices for the elements of the eqn{A} matrix.
• mod.P
  modification indices for the elements of the eqn{P} matrix.
• par.A
  estimated parameter changes for the elements of the eqn(A) matrix.
• par.P
  estimated parameter changes for the elements of the eqn(P) matrix.

Details

Modification indices are one-df chi-square score statistics for the fixed and constrained parameters in a structural equation model. They may be regarded as an estimate of the improvement in the likelihood-ratio chi-square statistic for the model if the corresponding parameter is respecified as a free parameter. The mod.indices function also estimates the change in the value of a fixed or constrained parameter if the parameter is respecified as free. When several parameters are set equal, modification indices and estimated changes are given for all but the first. Modification indices and estimated parameter changes for currently free parameters are given as NA. The method employed is described in Saris, Satorra, and S"{o}rbom (1987) and S"{o}rbom (1989).

References

Sarris, W. E., Satorra, A., and S"{o}rbom, D. (1987) The detection and correction of specification errors in structural equation models. Pp. 105--129 in Clogg, C. C. (ed.), Sociological Methodology 1987. American Sociological Association. S"{o}rbom, D. (1989) Model modification. Psychometrika 54, 371--384.

See Also

sem

Examples

# This example is adapted from the SAS manual

S.wh <- matrix(c(
   11.834,     0,        0,        0,       0,        0,
    6.947,    9.364,     0,        0,       0,        0,
    6.819,    5.091,   12.532,     0,       0,        0,
    4.783,    5.028,    7.495,    9.986,    0,        0,
   -3.839,   -3.889,   -3.841,   -3.625,   9.610,     0,
  -21.899,  -18.831,  -21.748,  -18.775,  35.522,  450.288), 
  6, 6)

model.wh <- matrix(c(
                    'Alienation67   ->  Anomia67',      NA,     1,
                    'Alienation67   ->  Powerless67',   NA,     0.833,
                    'Alienation71   ->  Anomia71',      NA,     1,
                    'Alienation71   ->  Powerless71',   NA,     0.833, 
                    'SES            ->  Education',     NA,     1,     
                    'SES            ->  SEI',           'lamb', NA,
                    'SES            ->  Alienation67',  'gam1', NA,
                    'Alienation67   ->  Alienation71',  'beta', NA,
                    'SES            ->  Alienation71',  'gam2', NA,
                    'Anomia67       <-> Anomia67',      'the1', NA,
                    'Anomia71       <-> Anomia71',      'the1', NA,
                    'Powerless67    <-> Powerless67',   'the2', NA,
                    'Powerless71    <-> Powerless71',   'the2', NA,
                    'Education      <-> Education',     'the3', NA,
                    'SEI            <-> SEI',           'the4', NA,
                    'Anomia67       <-> Anomia71',      'the5', NA,
                    'Powerless67    <-> Powerless71',   'the5', NA,
                    'Alienation67   <-> Alienation67',  'psi1', NA,
                    'Alienation71   <-> Alienation71',  'psi2', NA,
                    'SES            <-> SES',           'phi',  NA), 
                    ncol=3, byrow=TRUE)
                                            
obs.vars.wh <- c('Anomia67','Powerless67','Anomia71','Powerless71','Education','SEI')
rownames(S.wh) <- colnames(S.wh) <- obs.vars.wh

sem.wh <- sem(model.wh, S.wh, 932)

mod.indices(sem.wh)

##   5 largest modification indices, A matrix:
##  Powerless67:Education    Anomia67:Education 
##                 4.8736                3.8027 
##        Powerless67:SES Education:Powerless67 
##                 2.7608                2.4619 
##         Anomia67:SES 
##               2.3122 
##
##    5 largest modification indices, P matrix:
##  Education:Powerless67    Education:Anomia67 
##                 6.4028                4.5398 
##        SES:Powerless67          SES:Anomia67 
##                 2.7608                2.3122 
##        SEI:Powerless67 
##                 1.3185