Slide 8
Slide 8 text
Hierarchical models
Unpooled, linear regression
y ⇠ N(µ, )
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AAACCXicbVDLSsNAFJ3UV62vqEs3g61QQUrSjS6LblxJBfuAJpTJdNIOnZmEmYkQQrdu/BU3LhRx6x+482+ctFlo9cCFwzn3cu89Qcyo0o7zZZVWVtfWN8qbla3tnd09e/+gq6JEYtLBEYtkP0CKMCpIR1PNSD+WBPGAkV4wvcr93j2RikbiTqcx8TkaCxpSjLSRhjaspdBTlEOPIz3BiGU3s7rHkzMjjjk6rQ3tqtNw5oB/iVuQKijQHtqf3ijCCSdCY4aUGrhOrP0MSU0xI7OKlygSIzxFYzIwVCBOlJ/NP5nBE6OMYBhJU0LDufpzIkNcqZQHpjO/Vy17ufifN0h0eOFnVMSJJgIvFoUJgzqCeSxwRCXBmqWGICypuRXiCZIIaxNexYTgLr/8l3SbDddpuLfNauuyiKMMjsAxqAMXnIMWuAZt0AEYPIAn8AJerUfr2Xqz3hetJauYOQS/YH18A/HTmTM=
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AAACCXicbVDLSsNAFJ3UV62vqEs3g61QQUrSjS6LblxJBfuAJpTJdNIOnZmEmYkQQrdu/BU3LhRx6x+482+ctFlo9cCFwzn3cu89Qcyo0o7zZZVWVtfWN8qbla3tnd09e/+gq6JEYtLBEYtkP0CKMCpIR1PNSD+WBPGAkV4wvcr93j2RikbiTqcx8TkaCxpSjLSRhjaspdBTlEOPIz3BiGU3s7rHkzMjjjk6rQ3tqtNw5oB/iVuQKijQHtqf3ijCCSdCY4aUGrhOrP0MSU0xI7OKlygSIzxFYzIwVCBOlJ/NP5nBE6OMYBhJU0LDufpzIkNcqZQHpjO/Vy17ufifN0h0eOFnVMSJJgIvFoUJgzqCeSxwRCXBmqWGICypuRXiCZIIaxNexYTgLr/8l3SbDddpuLfNauuyiKMMjsAxqAMXnIMWuAZt0AEYPIAn8AJerUfr2Xqz3hetJauYOQS/YH18A/HTmTM=
AAACCXicbVDLSsNAFJ3UV62vqEs3g61QQUrSjS6LblxJBfuAJpTJdNIOnZmEmYkQQrdu/BU3LhRx6x+482+ctFlo9cCFwzn3cu89Qcyo0o7zZZVWVtfWN8qbla3tnd09e/+gq6JEYtLBEYtkP0CKMCpIR1PNSD+WBPGAkV4wvcr93j2RikbiTqcx8TkaCxpSjLSRhjaspdBTlEOPIz3BiGU3s7rHkzMjjjk6rQ3tqtNw5oB/iVuQKijQHtqf3ijCCSdCY4aUGrhOrP0MSU0xI7OKlygSIzxFYzIwVCBOlJ/NP5nBE6OMYBhJU0LDufpzIkNcqZQHpjO/Vy17ufifN0h0eOFnVMSJJgIvFoUJgzqCeSxwRCXBmqWGICypuRXiCZIIaxNexYTgLr/8l3SbDddpuLfNauuyiKMMjsAxqAMXnIMWuAZt0AEYPIAn8AJerUfr2Xqz3hetJauYOQS/YH18A/HTmTM=
AAACCXicbVDLSsNAFJ3UV62vqEs3g61QQUrSjS6LblxJBfuAJpTJdNIOnZmEmYkQQrdu/BU3LhRx6x+482+ctFlo9cCFwzn3cu89Qcyo0o7zZZVWVtfWN8qbla3tnd09e/+gq6JEYtLBEYtkP0CKMCpIR1PNSD+WBPGAkV4wvcr93j2RikbiTqcx8TkaCxpSjLSRhjaspdBTlEOPIz3BiGU3s7rHkzMjjjk6rQ3tqtNw5oB/iVuQKijQHtqf3ijCCSdCY4aUGrhOrP0MSU0xI7OKlygSIzxFYzIwVCBOlJ/NP5nBE6OMYBhJU0LDufpzIkNcqZQHpjO/Vy17ufifN0h0eOFnVMSJJgIvFoUJgzqCeSxwRCXBmqWGICypuRXiCZIIaxNexYTgLr/8l3SbDddpuLfNauuyiKMMjsAxqAMXnIMWuAZt0AEYPIAn8AJerUfr2Xqz3hetJauYOQS/YH18A/HTmTM=
Residuals distributed normally with
mean and standard dev
(x_i) = observation at i
µ = 1 + 2xi
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
Partial pooled regression
Mean (log) CBO of Controller in project i
alpha = intercept, Beta slope
Slope and intercept vary per project
y ⇠ N(↵j[i]
+ j[i]
xi, )
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
Aka multilevel models,
partial pooling models,
varying slope and intercept models