GEG 100 ONLINE!

Cultural Geography

Chapter 4
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 Newton's First Law of Migration: The Gravity Model

READ:

ACTIVITIES:

Read: pp. 94-98

Items to Hand In:

Activity 1: • The completed spreadsheet table for migration to Illinois

Activity 2: • The scatter diagram, including the labels of poorly predicted states

Activity 3: • The residual map - Be sure to type in a descriptive title

Activity 4: • Typed answers to questions 4.1–4.7

Estimated Time Requirements

Activity 1: Predicting Migration with the Gravity Model 15-30 minutes

Activity 2: Scatter Diagram of the Residuals 10-20 minutes

Activity 3: Residual Map 15-25 minutes

Activity 4: Evaluation 40-60 minutes

CONCEPTS / VOCABULARY

All "Keyterms"
  • Distance Decay: The declining intensity of an activity with increasing distance from its point of origin.

  • Extreme Value: A point on a scatter diagram that is roughly in line with the main trend but is separated from the main group of points because of its extremely high or low value.Contrast with outlier.
  • Gravity Model: A model to predict spatial interaction, where size (population) is directly related to interaction and distance is inversely related to interaction.
  • Migration: A permanent change in residence to outside one's community of origin.
  • Migration Selectivity: The tendency for certain types of people to migrate. Age, education, and other sociodemographic characteristics are migration selectivity factors.
  • Migration Stream: A well-defined migration channel from a specific origin to a particular destination.
  • Migration Counterstream: Migration that runs opposite to a migration stream.
  • Outlier: Point on a scatter diagram that lies far off the trend line. Outliers on the graph correspond to cases that are poorly predicted by the model. Outliers are not to be confused with extreme values, which may lie far from any other point but which are still close to the best-fitting line (see Figure 4.13).
  • Pull Factors: Reasons to move to a particular place.
  • Push Factors: Reasons to move from a particular place.
  • Residuals: The difference between an actual observed value of some variable and its predicted value using the gravity model.
  • Scatter Diagram: A scatter of dots showing the relationship between two variables. Each dot on the graph represents the x and y coordinates of a different observation or case.
  • Spatial Interaction: Movements of ideas, information, money, products, and people between places.

Plus:

  • local mover (87)
  • hinterland (87)
  • place desireability (87)
  • pioneer migrant (89)
  • Depression Era Dust bowl Migrants (89)
  • enclave (90)
  • refugee (90)
  • cubanidad (90)
  • self-compensating flows (90)
  • exponent (92)
  • numerator / denominator (93)
  • channelized migration = migration streams (89, 93)
  • net migration rates (97)

INSTRUCTOR'S NOTES and/or ADDITIONS TO TEXT READING

Chapter 4 is the most mathematical exercise that we have had so far. KNOW WHAT THE NUMBERS MEAN.

 

In activity 1 you are predicting the number of people who will migrate TO Illinois FROM each of the other 49 states. Your prediction is based on how far away each state is from Illinois and the number of people in each state.

Column E is the number of people you PREDICTED will migrate TO Illinois. Column F is the ACTUAL number who migrated TO Illinois from each state.

In Activity 3 you are creating a choropleth map. Think about where you want to set your "break points" (see chapter 1). We want to use the map to see where our model works well at predicting the actual migration TO Illinois and where the model does not work well. Be sure to move the vertical red bars that set the break points so that the break points make sense.

4.1 I didn't eliminate any extreme values. When I tried eliminating some to "spread out" the rest of the dots, it didn't make much of a difference.

4.2 I am not sure what "how close" means. Maybe it means something like how many states had a residual between -25 and +25 -- or how many states had a predicted value between 25% less than the actual and 25% more than the actual.

4.3 Think about this question and try to come up with many reasons that distance is a barrier to migration. Some are discussed in the textbook. Why do people tend to migrate a short distance rather than a long distance?

4.4 See textbook. Read it carefully - or read it again.

4.5 Make sure you know what the residual number means and what the difference is between a negative (-) residual and a positive (+) one.

4.6

The textbook in chapter 4, Activity 3, E, page 104, says to print your residual map and send it in with the assignment. The map that I want you to send in is the best map that you came up with according to part B on page 103. Do NOT send in the two-color map that they suggest that you try in part C.

You are going to use this map for question 4.6 (page 105). In this question you want to see WHERE are the states that were POORLY PREDICTED by the model. Where were the states that were GREATLY OVERPREDICTED and where were the states that were GREATLY UNDERPREDICTED?

 

Study the map. Circle the groups of states that are greatly UNDERPREDICTED (meaning that the residual is positive and more migrated to Illinois than our model predicted) and the groups of states that were OVERPREDICTED (meaning that fewer actually migrated from those states to Illinois than our model predicted), Then DESCRIBE THE SPATIAL PATTERN. This means tell me WHERE are those groups of states that were underpredicted and those that were overpredicted.

 

Then, try to come up with explanations of why our model based on distance and population was so wrong in predicting migration to Illinois from these groups of states. Read the textbook again to get ideas. Think about things like push factors, pull factors, migration streams, migration counterstreams, and migration selectivity. REMEMBER, the model ALREADY considers distance and population of the sending state, but it still underpredicted or overpredicted groups of states. Why? QUESTIONS? Use the Discussion Forum.

 

4.7 The answer to this is based on your answer to #4.6 Once you figure out which states were poorly predicted by the model, THEN try to figure out what variable you might add to the formula (in addition to population and distance) to make the predictions more accurate. ALSO CONSIDER if you would put your new variables in the NUMERATOR (meaning that this variable results in more people migrating to Illinois) or in the DENOMINATOR (meaning that this variable results in fewer people migrating to Illinois).

CHAPTER OUTLINE

I. Spatial interaction is movement from place to place. What forms can spatial interaction take?
  1. Migration
  2. Commuting
  3. Transportation of goods
  4. Movement of ideas through telephone calls, fax messages, and the Internet
  5. Transfers of money

II. Migration

  1. I. Places are connected through spatial interaction. Interactions can be movements of

    1. Ideas

    2. Information

    3. Money

    4. Products

    5. People

     

    II. Migration

    1. 1. Defined as permanent change in residence to outside one's community of origin

      2. Spatial scale and migration

      3. Factors of place desirability

      4. Immigration as special case of migration across international borders

      1. a. remittances

        b. refugees as special case of immigrant-threat of persecution

      5. Push and pull factors

      6. Migration selectivity factors (age, education, length of residence)

       

    7..Distance decay

    8. Migration streams and counterstreams

    1. Examples: Dustbowl migrants, immigrants to enclaves, Cuban-born and Mexican-born immigrants

III The gravity model: PREDICTING MIGRATION FLOWS

  1. What is a model?: a simplified representation of reality
  2. The gravity model was adapted from the physical sciences where it is used to show the attraction between two masses.
  3. The gravity model was adapted to the social sciences to show spatial interaction between two places.
  4. Mathematical formulation
    1. a. Size or mass variables in the numerator
      b. Distance variable in the denominator
      c. Distance exponent-measures the drag, or impedance, of
      distance on interaction
      d. k-factor

       
  • is a measure of the amount of predicted interaction between two places, the origin i and the destination j
    • the larger Iij is, the more interaction is predicted
  • Size or mass variables in the numerator --- and --- often population
    • The greater the population, the greater the interaction
  • Distance variable in the denominator ---
    • The greater the distance, the smaller the interaction
  • Distance exponent ( ) measures the drag, or impedance, of distance on interaction.
    • the greater the distance exponent, the smaller the interaction
    • the greater the distance exponnent, the quicker, or steeper, the distance decay
    • students will ignore this in the activities
  • k-factor or scaling constant---
    • depends on the type of interaction being predicted
    • students will be given this in the activities

     

  1. Think critically about modeling human behavior

IV. Mobility

  1. Part of the American experience
  2. High in developed countries
  3. Strong predictor of whether person will move in the future is whether they have moved in the past
  4. Currently a lower rate of U.S. mobility than in earlier decades

  5. Regional differences in mobility rates: - WHY?
    • US 15.9 %
    • Northeast 11.7 %
    • Midwest 15.1%
    • South 17.1 %
    • West 18.5 %
  6. Regional and sub-regional shifts in population - WHY?

  7. Net migration
  8. Today’s migration patterns reflect:
    • the location of states relative to one another (nearby states tend to exchange migrants)
    • historical patterns of movement (i.e. longtime linkages between Florida and New York and between California and Texas)
    • the changing geography of economic opportunity in the nation
    • the public’s perceptions about the attractiveness of places, including intangibles like an agreeable climate, being near family and friends, and a good view.

V. The mechanics of the assignment in Activities 1, 2, and 3

  1. Spreadsheets allow easy calculation of an entire series of numbers in a few simple steps. Scatter diagrams allow us to plot actual versus expected migration.
  2. Outliers are states that deviate from the 45-degree line on the scatter diagram.
  1. Residuals show errors in the predicted values.

 

INSTRUCTOR'S NOTES and/or ADDITIONS TO ACTIVITIES

 From the Instructor's Manual:
We recommend you do not skip any parts of this exercise. The material is cumulative in the sense that Activity 2 builds upon Activity 1, Activity 3 builds upon Activities 1 and 2, and so on. Activity 1 involves simple spreadsheet mechanics, but it provides the raw material for the critical thinking that comes in analyzing the scatter diagram in Activity 2 and analyzing residuals in Activity 3. Activities 1, 2, and 3 are necessary for evaluating the ability of the gravity model to predict migration flows and for suggesting revisions to the model that enhance its predictive ability in Activity 4. You may wish to tell students to look at the questions in Activity 4 before they complete and exit out of Activities 1 to 3. This will help them think about what they are doing in the first 3 activities.

Activities 1–3 use the CD. This can be done individually or in groups, in a computer lab or outside of class. In using the CD, students gain experience interrelating spatial information from a spreadsheet (Activity 1), a scatter diagram (Activity 2), and a residual map (Activity 3). We recommend that you demonstrate Activities 1 though 3 using a computer projection system if one is available. You can do so without giving away the answers by demonstrating the functionality with a different state. If you are in California, try using Oregon or Florida as your example.

In Activity 4, students respond to a series of open-ended questions about the gravity model’s ability to predict migration to their state. For most U.S. states and Canadian provinces, the gravity model is only a mediocre predictor of migration. The fun and challenge of the activity is in identifying the outliers—the states and provinces that are poorly predicted—and in figuring out how the model can be modified so that it works better. Think of the gravity model as a straw man. We are trying to knock it down and pick it apart. It helps to emphasize that the gravity model reveals something, but not everything, about migration.

You may wish to preface this exercise with a discussion of migration to your state or province:

  • Why might some states send more migrants to your state than others?
  • What do you think will be the major sending areas for migrants to your state? Why?

 

 

Mij = gravity model prediction of migration between origin i and destination j
Pi = population of origin state i
dij = distance from origin i to destination j
k = a constant that adjusts the gravity model estimates so that the total numbers of actual and estimated migrants are approximately equal

 

 

WEB RESOURCES

U.S. Census Bureau. Geographic Mobility And Migration Page: http://www.census.gov/population/www/socdemo/migrate.html.

Migration Research Unit at the University College, London: http://www.geog.ucl.ac.uk/mru/.