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Population Marginal Means

Population Marginal Means. Two factor model with replication. Population Marginal Means. Population Marginal Means. The above expectation depends on the design Population marginal means depend only on the unknown parameters; it is these quantities that LSMEANS estimates.

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Population Marginal Means

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  1. Population Marginal Means • Two factor model with replication

  2. Population Marginal Means

  3. Population Marginal Means • The above expectation depends on the design • Population marginal means depend only on the unknown parameters; it is these quantities that LSMEANS estimates

  4. Population Marginal Means

  5. Missing CellsPopulation Marginal Means • Additive two factor model with replication • Example from Searle • a=2, b=2, n22=0 • Searle et al use unusual constraints—choice of constraints doesn’t affect estimators for either the observed or unobserved cell means

  6. Missing CellsPopulation Marginal Means • Table of expectations (note that 22= 12+ 21- 11)

  7. Missing CellsPopulation Marginal Means • Table of least squares estimates

  8. Population Marginal Means • LSMEANS for the population marginal means: LSMEANS

  9. Missing CellsPopulation Marginal Means • Table of expectations for the interaction model

  10. Missing CellsEstimability • Table of least squares estimates for the interaction model • PMM(2), PMM(2), PMM(22) are also non-estimable

  11. Missing CellsEstimability • Worksheet Example • Yandell notes that cell means in an additive model are always estimable if the design is connected • Connectedness is easy to verify in a two-way layout; difficult in other contexts.

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