Dref | R Documentation |

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.

`gnm`

, `formula`

,
`nonlin.function`

### 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 ## End(Not run)

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