Specify a Diagonal Reference Term in a gnm Model Formula
Dref is a function of class "nonlin" to specify a diagonal
reference term in the formula argument to gnm.
Dref(..., delta = ~ 1)
... |
a comma-separated list of two or more factors. |
delta |
a formula with no left-hand-side specifying the model for each factor weight. |
Dref specifies diagonal reference terms as introduced by
Sobel (1981, 1985). Such terms comprise an additive component for
each factor of the form
w_f gamma_l
where w_f is the weight for factor f, gamma_l is the diagonal effect for level l and l is the level of factor f for the given data point.
The weights are constrained to be nonnegative and to sum to one as follows
w_f = exp(delta_f)/sum_i(exp(delta_i))
and the delta_f are modelled as specified by the
delta argument (constant weights by default). The
returned parameters are those in the model for
delta_f, rather than the implied weights
w_f. The DrefWeights function will take a fitted gnm
model and return the weights w_f, along with their standard
errors.
If the factors passed to Dref do not have exactly the same
levels, the set of levels in the diagonal reference term is taken to
be the union of the factor levels, sorted into increasing order.
A list with the anticipated components of a "nonlin" function:
predictors |
the factors passed to |
common |
an index to specify that common effects are to be estimated across the factors. |
term |
a function to create a deparsed mathematical expression of the term, given labels for the predictors. |
start |
a function to generate starting values for the parameters. |
call |
the call to use as a prefix for parameter labels. |
Heather Turner
Sobel, M. E. (1981), Diagonal mobility models: A substantively motivated class of designs for the analysis of mobility effects. American Sociological Review 46, 893–906.
Sobel, M. E. (1985), Social mobility and fertility revisited: Some new models for the analysis of the mobility effects hypothesis. American Sociological Review 50, 699–712.
Clifford, P. and Heath, A. F. (1993) The Political Consequences of Social Mobility. J. Roy. Stat. Soc. A, 156(1), 51-61.
Van der Slik, F. W. P., De Graaf, N. D and Gerris, J. R. M. (2002) Conformity to Parental Rules: Asymmetric Influences of Father's and Mother's Levels of Education. European Sociological Review 18(4), 489 – 502.
### Examples from Clifford and Heath paper
### (Results differ slightly - possible transcription error in
### published data?)
set.seed(1)
## reconstruct counts voting Labour/non-Labour
count <- with(voting, percentage/100 * total)
yvar <- cbind(count, voting$total - count)
## fit diagonal reference model with constant weights
classMobility <- gnm(yvar ~ -1 + Dref(origin, destination),
family = binomial, data = voting)
DrefWeights(classMobility)
## create factors indicating movement in and out of salariat (class 1)
upward <- with(voting, origin != 1 & destination == 1)
downward <- with(voting, origin == 1 & destination != 1)
## fit separate weights for the "socially mobile" groups
socialMobility <- gnm(yvar ~ -1 + Dref(origin, destination,
delta = ~ 1 + downward + upward),
family = binomial, data = voting)
DrefWeights(socialMobility)
## fit separate weights for downwardly mobile groups only
downwardMobility <- gnm(yvar ~ -1 + Dref(origin, destination,
delta = ~ 1 + downward),
family = binomial, data = voting)
DrefWeights(downwardMobility)
## Not run:
### Examples from Van der Slik paper
### For illustration only - data not publically available
### Using data in data.frame named 'conformity', with variables
### MCFM - mother's conformity score
### FCFF - father's conformity score
### MOPLM - a factor describing the mother's education with 7 levels
### FOPLF - a factor describing the father's education with 7 levels
### AGEM - mother's birth cohort
### MRMM - mother's traditional role model
### FRMF - father's traditional role model
### MWORK - mother's employment
### MFCM - mother's family conflict score
### FFCF - father's family conflict score
set.seed(1)
## Models for mothers' conformity score as specified in Figure 1
A <- gnm(MCFM ~ -1 + AGEM + MRMM + FRMF + MWORK + MFCM +
Dref(MOPLM, FOPLF), family = gaussian, data = conformity,
verbose = FALSE)
A
## Call:
## gnm(formula = MCFM ~ -1 + AGEM + MRMM + FRMF + MWORK + MFCM +
## Dref(MOPLM, FOPLF), family = gaussian, data = conformity,
## verbose = FALSE)
##
## Coefficients:
## AGEM MRMM
## 0.06363 -0.32425
## FRMF MWORK
## -0.25324 -0.06430
## MFCM Dref(MOPLM, FOPLF)delta1
## -0.06043 -0.33731
## Dref(MOPLM, FOPLF)delta2 Dref(., .).MOPLM|FOPLF1
## -0.02505 4.95121
## Dref(., .).MOPLM|FOPLF2 Dref(., .).MOPLM|FOPLF3
## 4.86329 4.86458
## Dref(., .).MOPLM|FOPLF4 Dref(., .).MOPLM|FOPLF5
## 4.72343 4.43516
## Dref(., .).MOPLM|FOPLF6 Dref(., .).MOPLM|FOPLF7
## 4.18873 4.43378
##
## Deviance: 425.3389
## Pearson chi-squared: 425.3389
## Residual df: 576
## Weights as in Table 4
DrefWeights(A)
## Refitting with parameters of first Dref weight constrained to zero
## $MOPLM
## weight se
## 0.4225636 0.1439829
##
## $FOPLF
## weight se
## 0.5774364 0.1439829
F <- gnm(MCFM ~ -1 + AGEM + MRMM + FRMF + MWORK + MFCM +
Dref(MOPLM, FOPLF, delta = ~1 + MFCM), family = gaussian,
data = conformity, verbose = FALSE)
F
## Call:
## gnm(formula = MCFM ~ -1 + AGEM + MRMM + FRMF + MWORK + MFCM +
## Dref(MOPLM, FOPLF, delta = ~1 + MFCM), family = gaussian,
## data = conformity, verbose = FALSE)
##
##
## Coefficients:
## AGEM
## 0.05818
## MRMM
## -0.32701
## FRMF
## -0.25772
## MWORK
## -0.07847
## MFCM
## -0.01694
## Dref(MOPLM, FOPLF, delta = ~ . + MFCM).delta1(Intercept)
## 1.03515
## Dref(MOPLM, FOPLF, delta = ~ 1 + .).delta1MFCM
## -1.77756
## Dref(MOPLM, FOPLF, delta = ~ . + MFCM).delta2(Intercept)
## -0.03515
## Dref(MOPLM, FOPLF, delta = ~ 1 + .).delta2MFCM
## 2.77756
## Dref(., ., delta = ~ 1 + MFCM).MOPLM|FOPLF1
## 4.82476
## Dref(., ., delta = ~ 1 + MFCM).MOPLM|FOPLF2
## 4.88066
## Dref(., ., delta = ~ 1 + MFCM).MOPLM|FOPLF3
## 4.83969
## Dref(., ., delta = ~ 1 + MFCM).MOPLM|FOPLF4
## 4.74850
## Dref(., ., delta = ~ 1 + MFCM).MOPLM|FOPLF5
## 4.42020
## Dref(., ., delta = ~ 1 + MFCM).MOPLM|FOPLF6
## 4.17957
## Dref(., ., delta = ~ 1 + MFCM).MOPLM|FOPLF7
## 4.40819
##
## Deviance: 420.9022
## Pearson chi-squared: 420.9022
## Residual df: 575
##
##
## Standard error for MFCM == 1 lower than reported by Van der Slik et al
DrefWeights(F)
## Refitting with parameters of first Dref weight constrained to zero
## $MOPLM
## MFCM weight se
## 1 1 0.02974675 0.2277711
## 2 0 0.74465224 0.2006916
##
## $FOPLF
## MFCM weight se
## 1 1 0.9702532 0.2277711
## 2 0 0.2553478 0.2006916
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