Sociology 388, Log-Linear Models

 

Fall Quarter, 2007

 

Professor Michael J. Rosenfeld

mrosenfe@stanford.edu

http://www.stanford.edu/~mrosenfe

(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

 

 

 

Introduction:

            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, http://www.stanford.edu/~mrosenfe.

            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 http://www.stata.com/.  Copies of the STATA manuals are available in the Meyer library, and in the Sociology Department computer cluster.

 

 

 

Grading:

 

Due

Pct of final grade

Homework 1

Tuesday, October 9, in class

15%

Homework 2

Thursday, October 18, in class

15%

Homework 3

Tuesday, October 30, in class

20%

Paper abstract

Tuesday, November 6

0%

Paper Draft

Thursday, November 15

10%

Final Paper

In class Thursday, December 6

40%

 

 

 

Two examples of Cross tabulated data:

 

1)Occupation by Race

 

 

Race

 

 

 

White

Non White

Occupational Class

Other

42,012

7,146

 

White Collar

17,216

2,361

 

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

 

 

Wives

 

 

 

 

Husbands:

NH Black

Mexican

Other Hisp

All Others

NH White

Non Hisp Black

4074

63

32

42

215

Mexican

25

3947

143

95

1009

Other Hispanic

16

132

239

18

304

All Others

19

78

18

1022

360

Non Hisp White

103

1156

373

492

28453

 

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.