rpm-terms {rpm}

Terms used in a Revealed Preference Matchings Model

Description

The function rpm is used to fit a revealed preference model for men and women of certain characteristics (or shared characteristics) of people of the opposite sex. The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities. It does this using an large-population likelihood based on ideas from Dagsvik (2000), Menzel (2015) and Goyal et al (2023).

Details

The model represents the dyadic utility functions as deterministic linear utility functions of dyadic variables. These utility functions are functions of observed characteristics of the women and men. These functions are entered as terms in the function call to rpm. This page describes the possible terms (and hence linear utility functions) included in rpm package.

Value

No return value, called for side effects.

Specifying models

Terms to rpm are specified by a formula to represent the pairings and covariates This is done via a formula, that is, an formula object, of the form ~ <term 1> + <term 2> ..., where <term 1>, <term 2>, etc, are each terms chosen from the list given below.

absdiff(attr) (quantitative attribute), absdiff(attr) (quantitative attribute)

Absolute difference: The attr argument specifies a quantitative attribute This term adds one statistic to the model equaling abs(attr[i]-attr[j]) for all women-man dyad (i,j).

W_greaterthan(attr)

Women's value greater than the men's value Adds one statistic indicating if the women's value exceeds the men's value.

M_greaterthan(attr)

Men's value greater than the women's value Adds one statistic indicating if the men's value exceeds the women's value.

W_atleast(attr,threshold=0)

Values greater than or equal to a threshold Adds one statistic indicating if the women's value of the attribute equals or exceeds threshold.

W_atmost(threshold=0)

Values less than or equal to a threshold Adds one statistic indicating if the women's value equals or is exceeded by threshold.

W_cov(attr) (quantitative attribute), W_cov(attr) (quantitative attribute)

Main effect of a covariate for women: The attr argument specifies a quantitative attribute This term adds a single statistic equaling the value of attr(i) for women i in the dyad. For categorical attributes, see W_factor.

diff(attr) (quantitative attribute), diff(attr) (quantitative attribute)

Woman's Gap: The attr argument specifies a quantitative attribute This term adds one statistic to the model being attr[i]-attr[j] for women i and man j. Specifically, it is the excess of the woman's value over the man's value.

WtoM_diff(attr, diff) (ordinal categorical attribute), WtoM_diff(attr) (ordinal categorical discrete attribute)

Woman's Gap: The attr argument specifies a ordinal categorical attribute This term adds one statistic to the model being an indicator that attr[i]=attr[j]+diff for women i and man j. Specifically, it indicates if the woman's value is diff higher than the man's value.

MtoW_diff(attr, diff) (ordinal categorical attribute), MtoW_diff(attr) (ordinal categorical discrete attribute)

Man's Gap: The attr argument specifies a ordinal categorical attribute This term adds one statistic to the model being an indicator that attr[j]=attr[i]+diff for women i and man j. Specifically, it indicates if the man's value is diff higher than the woman's value.

MtoW_diff(attr) (quantitative attribute), MtoW_diff(attr) (quantitative attribute)

Difference: The attr argument specifies a quantitative attribute This term adds one statistic to the model attr[j]-attr[i] for women i and man j.

W_factor(attr, base=1, levels=-1) (categorical attribute), W_factor(attr, base=1, levels=-1) (categorical attribute)

Factor attribute effect for women: The attr argument specifies a categorical attribute This term adds multiple statistics to the model, one for each of (a subset of) the unique values of the attr attribute. Each of these statistics indicates if the women's has that attribute.

homophily(attr)

Uniform homophily effect: The attr argument specifies a categorical attribute This term adds one statistic to the model indicating that the dyad matches on that attribute.

match(attr, diff=FALSE, collapse=NULL)

Attribute-based homophily effect: The attr argument specifies a categorical attribute This term adds one statistic to the model for each categorical level, unless diff is set to TRUE, in which case the term adds multiple statistics to the model, one for each of (a subset of) the unique values of the attr attribute. If diff is set to TRUE, the optional argument collapse control what dyads are collapsed (or pooled). Specifically, it is a list of indices of attribute values which are to be collapsed into a single term. For example, collapse=list(c(1,4)) will collapse the (1,1) and the (4,4) dyads into a single term (and group). Multiple lists can be included with arbitrary numbers of dyads in a group.

mix(attr, base=NULL, collapse=NULL)

Attribute mixing: The attr argument specifies a categorical attributes By default, this term adds one statistic to the model for each possible pairing of attribute values. The statistic indicates if the dyad has that pairing of values. In other words, this term produces one statistic for every entry in the mixing matrix for the attribute(s). The ordering of the attribute values is lexicographic: alphabetical (for nominal categories) or numerical (for ordered categories). The optional argument base control what statistics are included in the model, specifically it lists the index of the omitted terms (in order). For example, base=2 omits the second term. The optional argument collapse control what dyads are collapsed (or pooled). Specifically, it is a list of lists. Each element of the list is a list of dyads which are to be collapsed into a single term. For example, collapse=list(list(c(1,4),c(2,4))) will collapse the (1,4) and the (2,4) dyads into a single term (and group). Multiple lists can be included with arbitrary numbers of dyads in a group.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review,, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

See Also

rpm package, rpm

Examples

library(rpm)
data(fauxmatching)

fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled")
summary(fit)