Sociology 388, Log-Linear Models


Fall Quarter, 2007


Professor Michael J. Rosenfeld

(650) 723-3958

Office Hours: Tuesdays and Thursdays 3:10-3:40



Class meets Tuesdays and Thursdays 11:00 AM- 11:50 AM

Building 160, Room B36





            This class is restricted to graduate students, with preference to doctoral students in the sociology department.

            This class should provide students with theoretical and practical knowledge of how to analyze categorical data, and how to interpret and understand the results of that analysis.  The class will start with the simplest case- a 2x2 table, and work up to more complicated datasets and models.  We will start with odds ratios calculated by hand, and move on to loglinear and logistic regression models.  We will discuss log linear models for ordinal and nominal categories.  We will discuss measures of goodness-of-fit.  We will discuss broader issues, such as how to incorporate detailed statistical results into a straightforward argument. 

            Towards the end of the class I will introduce a variety of alternatives to loglinear models, and explain their uses.  We will discuss negative binomial models and log multiplicative models.  We will discuss error structure, and alternate ways to estimate the errors of parameters including robust standard errors, and the bootstrap.

            Most of the lectures and assignments will rely on the statistical package Stata.  The sociology department computer cluster has licenses of Stata 9, including the freeware module desmat. The sociology computer cluster also has the freeware Windows-only program LEM, which we will use for log-multiplicative models.  Regular class meetings will take place in Meyer library 143, which is a Mac lab.  Early assignments will also emphasize the use of the spreadsheet Excel, which will allow students to work with simple models directly.  I will post notes and homework answers on my website,

            Grading will be based on homework, and a final paper.


Required Readings (Available at Stanford Bookstore):

            Agresti, Alan.  1996.  An Introduction to Categorical Data Analysis.  New York: Wiley.

            Hout, Michael:  1983.  Mobility Tables.  Beverly Hills: Sage Press.


Recommended Reading:

            Agresti, Alan.  1990.  Categorical Data Analysis.  New York:  Wiley.


            Also: Students are expected to have some familiarity with STATA, and I will explain in detail how to use the small number of commands that are relevant to this class.  Students may want, however, to purchase the reference guide to STATA, or the introduction to STATA, or the software itself (to run on your own machine).  See  Copies of the STATA manuals are available in the Meyer library, and in the Sociology Department computer cluster.







Pct of final grade

Homework 1

Tuesday, October 9, in class


Homework 2

Thursday, October 18, in class


Homework 3

Tuesday, October 30, in class


Paper abstract

Tuesday, November 6


Paper Draft

Thursday, November 15


Final Paper

In class Thursday, December 6





Two examples of Cross tabulated data:


1)Occupation by Race








Non White

Occupational Class





White Collar




source: 2000 CPS, nationally representative data, unweighted



This table has one ordinal dimension (occupational class) and one nominal dimension (race).  Some simple questions:  Are Whites overrepresented in White collar jobs?  Are non-Whites underrepresented in the more desirable jobs?  How great is this underrepresentation or overrepresentation, and how significant is it?



2) Husband's Race by Wife's Race









NH Black


Other Hisp

All Others

NH White

Non Hisp Black












Other Hispanic






All Others






Non Hisp White







source: 1990 Census PUMS for Los Angeles County


This table has symmetric, nominal categories.  Some questions will be: Is the tendency to endogamy equally strong in all racial and ethnic groups?  Which kinds of intermarriage are especially unlikely, or especially likely?  What different kinds of models fit the data well, and by which standard of goodness of fit?  What kinds of gender effects are evident in racial intermarriage?



Additional Reading



1) Some Other Useful General References on the Methodology of Loglinear Models:


Bishop, Yvonne M.M., Stephen E. Fienberg and Paul W. Holland.  Discrete Multivariate Analysis:  Theory and Practise.  Cambridge, MA: MIT Press.


Clogg, Clifford C. and Scott R. Eliason. 1987. "Some Common Problems in Log-Linear Analysis" Sociological Methods and Research 16: 8-44.


Clogg, Clifford C. and Edward S. Shihadeh.  1994.  Statistical Models for Ordinal Variables.  Thousand Oaks, California:  Sage Press.


Long, J. Scott.  1997.  Regression Models for Categorical and Limited Dependent Variables.  Thousand Oaks, CA: Sage Press


Long, J. Scott and Jeremy Freese.  2001.  Regression Models for Categorical Dependent Variables Using STATA.  College Station, TX: STATA Press.



2) Additional Readings on Statistics with STATA


Long, J. Scott and Jeremy Freese.  2001.  Regression Models for Categorical Dependent Variables Using STATA.  College Station, TX: STATA Press.


Hamilton, Lawrence C.  2001.  Statistics with Stata.  Duxbury Press.



3) Examples of Articles that use Loglinear Models with Intermarriage Data:

Botev, Nikolai.  1994.  "Where East Meets West: Ethnic Intermarriage in the Former Yugoslavia"  American Sociological Review 59: 461-480


Fu, Vincent Kang.  2001.  "Racial Intermarriage Pairings".  Demography 38: 147-159


Hout, Michael and Joshua Goldstein.  1994. "How 4.5 Million Irish Immigrants Became 40 Million Irish Americans: Demographic and Subjective Aspects of Ethnic Composition of White Americans" American Sociological Review 59: 64-82


Kalmijn, Matthijs.  1991a.  "Shifting Boundaries: Trends in Religious and Educational Homogamy" American Sociological Review 56: 786-800


Kalmijn, Matthijs.  1991b.  "Status Homogamy in the United States" American Journal of Sociology" 97: 496-523


Kalmijn, Matthijs.  1993.  "Trends in Black/White Intermarriage."  Social Forces 72: 119-146


Pagnini, Deanna L. and S. Philip Morgan.  1990.  "Intermarriage and Social Distance among U.S. Immigrants at the turn of the Century."  American Journal of Sociology 96 (2): 405- 432


Qian, Zenchao.  1997.  'Breaking Racial Barriers:  Variations in Interracial Marriage Between 1980 and 1990' Demography 34: 263- 276


Rosenfeld, Michael J.  2001.  "The Salience of Pan- National Hispanic and Asian Identities, in U.S. Marriage Markets", Demography 38: 161-175


Rosenfeld, Michael J.  2002.  "Measures of Assimilation in the Marriage Market: Mexican Americans 1970-1990",  Journal of Marriage and the Family 64: 152-162


Rosenfeld, Michael J.  2005. "A Critique of Exchange Theory in Mate Selection." American Journal of Sociology 110 (5) 1284-1325


Sandefur, Gary and Trudy McKinnell.  1986.  "American Indian Intermarriage" Social Science Research 15: 347-371



4) Examples of Papers that Use Loglinear Models with Data Other Than Intermarriage Data:


Bearman, Peter.  1997.  "Generalized Exchange."  American Journal of Sociology 102 (5): 1383-1415


Bearman, Peter S. and Glenn Deane.  1992.  "The Structure of Opportunity: Middle Class Mobility in England 1548-1689." American Journal of Sociology 98 (1) 30-66


Biblarz, Timothy J. and Adrian E. Raftery.  1993.  "The Effects of Family Disruption on Social Mobility."  American Sociological Review 58 (1) 97-109


Hogan, Dennis P. and Evelyn M. Kitagawa.  1985.  "The Impact of Social Status, Family Structure, and Neighborhood on the Fertility of Black Adolescents."  American Journal of Sociology 90 (4): 925-855


Lewin-Epstien, Noah and Moshe Semyonov.  1986.  "Ethnic Group Mobility in the Israeli Labor Market." American Sociological Review 51 (3) 342-452


Lichter, Daniel T.  1988.  "Racial Differences in Underemployment in American Cities."  American Journal of Sociology 93 (4): 771-792


Morgan, S. Philip and Ronald R. Rindfuss.  1985.  "Marital Disruption: Structural and Temporal Dimensions."  American Journal of Sociology 90 (5): 1055-1077


Weil, Frederick D.  1987.  "Cohorts, Regimes and the Legitimation of Democracy: West Germany Since 1945".  American Sociological Review 52 (3): 308-324


Western, M and EO Wright.  1994.  "The Permeability of Class Boundaries to Intergenerational Mobility Among Men in the US, Canada, Norway and Sweden" American Sociological Review 59: 606-629


Wright, Erik Olin and Donmoon Cho.  1992.  "The Relative Permeability of Class Boundaries to Cross-Class Friendships:  A Comparative Study of the United States, Canada, Sweden and Norway."  American Sociological Review.  57 (1): 85-102.



5) Some Examples of the Application of Log Multiplicative Models


Charles, Maria and David B. Grusky.  1995.  "Models for Describing the Underlying structure of Sex Segregation." American Journal of Sociology 100: 931-971.


David B. Grusky and Maria Charles. 1998. "The Past, Present and Future of Sex Segregation Methodology" Demography 35: 497-504.


Hout, M.  1988.  "More Universalism, Less Structural Mobility- The American Occupational Structure in the 1980s" American Journal of Sociology 93: 1358-1400


Stier, Haya and David B. Grusky.  1990.  "An Overlapping Persistence Model of Career Mobility."  American Sociological Review 55: 736-756


Xie, Yu.  1992.  "The Log-Multiplicative Layer Effect Model for Comparing Mobility Tables", American Sociological Review 57: 380-395




6) Literature on the BIC as an Alternative to the LRT for Model Selection


Raftery, Adrian.  1986.  'Choosing Models for Cross- Classifications'.  American Sociological Review 51: 145- 146


Weakliem, David L.  1999.  "A Critique of the Bayesian Information Criterion for Model Selection" Sociological Methods and Research 27 (3): 359- 397


Xie, Yu.  1999.  "The Tension Between Generality and Accuracy".  Sociological Methods and Research 27 (3): 428- 435



7) General Literature on Log-Multiplicative Models


Clogg, Clifford C. and Edward S. Shihadeh.  1994.  Statistical Models for Ordinal Variables.  Thousand Oaks, California:  Sage Press.


Goodman, Leo A.  1984.  The Analysis of Cross-Classified Data Having Ordered Categories.  Cambridge, MA:  Harvard University Press.


Goodman, Leo A.  1979.  Measures of Association for Cross Classifications.  New York:  Springer- Verlag.



8) Literature On Negative Binomial Models and Other Models for Count Data:


Cameron, A. Colin and Pravin K. Trivedi.  1986.  "Econometric Models Based on Count Data:  Comparisons and Applications of Some Estimators and Tests."  Journal of Applied Econometrics.  1 (1) 29-53


Cameron, A. Colin and Pravin K. Trivedi.  1998.  Regression Analysis of Count Data.  Cambridge University Press.


Hannan, Michael T.  1991.  "Theoretical and Methodological Issues in Analysis of Density- Dependent Legitimation in Organizational Evolution."  Sociological Methodology 21: 1-42.


King, Gary.  1989.  "Variance Specification in Event Count Models: From Restrictive Assumptions to a Generalized Estimator." American Journal of Political Science 33 (3): 762-784


Long, J. Scott.  1997.  Regression Models for Categorical and Limited Dependent Variables.  Thousand Oaks, CA: Sage Press



9) Literature on Robust Standard Errors


Huber, Peter J.  1967.  "The Behavior of Maximum Likelihood Estimates under Non-Standard Conditions".  Pages 221-233 in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability.  Berkeley, CA


Long, J. Scott and Laurie H. Ervin.  2000.  "Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model."  The American Statistician 54: 217-224


White, Halbert.  1980.  "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity".  Econometrica 48: 817-830


White, Halbert.  1981.  "Consequences and Detection of Misspecified Nonlinear Regression Models."  Journal of the American Statistical Association 76: 419-433


White, Halbert.  1982.  "Maximum Likelihood Estimation of Misspecified Models."  Econometrica 50: 1-25.



10) Literature on the Bootstrap


Efron, Bradley.  1979.  "Bootstrap Methods:  Another Look at the Jackknife."  Annals of Statistics 7 (1): 1-26


Efron, Bradley and Robert J. Tibshirani.  1994.  An Introduction to the Bootstrap.  CRC Press.