Insights into the UK Housing Market
On the UK housing market including property ownership, mortgage trends, house prices, demographics, and government initiatives such as Help to Buy schemes. Discover the challenges facing the market and the impact on homebuyers.
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Importance Many stock parameters are annual rates. e.g., growth & mortality (components of yield) time must be recorded. Usually as the age of the fish. Age assessment is vitally important. It is also EXPENSIVE! 2 Age Analysis
Concept Overall Have a large sample of fish. Measure length on all fish. Choose a portion of sample to assign age. Called the age sample. Fish chosen either in proportion to the number of fish in each length category as a fixed number per each length category (more common) Fish that are not aged are called the length sample. Develop relationship between age and length from fish in age sample. two-way contingency table called an age-length key Assign age to fish in length sample with age- length key . 3 Age Length Key
Concept Age-Length Key Use 10-cm intervals for length categories Make raw contingency table Age LCat 1 2 3 20 30 40 50 2 2 0 Age Sample len age 22 1 24 1 26 2 27 2 30 1 32 2 34 2 39 3 40 1 44 2 46 3 49 3 52 2 53 2 55 3 56 3 LCat 20 20 20 20 30 30 30 30 40 40 40 40 50 50 50 50 2 2 1 1 1 0 1 2 2 Convert to row-proportions table Age LCat 1 2 3 20 30 40 50 0.00 0.50 0.50 0.25 0.00 0.25 0.50 0.25 0.25 0.50 0.50 0.50 4 Age Length Key
Concept Age-Length Key Age-Length Key (as a reminder) LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50 Use 10-cm intervals for length categories Length Sample len age 23 25 26 28 32 33 36 40 43 44 48 49 51 54 Age LCat 20 20 20 20 30 30 30 40 40 40 40 40 50 50 Create length distribution LCat 20 30 40 50 Freq 4 3 5 2 5 Age Length Key
Concept Age-Length Key Age-Length Key (as a reminder) LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50 Length Sample len age 23 25 26 28 32 33 36 40 43 44 48 49 51 54 LCat 20 20 20 20 30 30 30 40 40 40 40 40 50 50 1 2 2 1 Length distribution (as a reminder) LCat 20 30 40 50 Freq 4 3 5 2 Identify number in each length category to be assigned each age 20-cm 4*0.5 = 2 age-1 4*0.5 = 2 age-2 4*0 = 0 age-3 Randomly determine which fish are assigned these ages. 6 Age Length Key
Concept Age-Length Key Age-Length Key (as a reminder) LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50 Length Sample len age 23 25 26 28 32 33 36 40 43 44 48 49 51 54 LCat 20 20 20 20 30 30 30 40 40 40 40 40 50 50 1 2 2 1 Length distribution (as a reminder) LCat 20 30 40 50 Freq 4 3 5 2 Identify number in each length category to be assigned each age 30-cm 3*0.25 = 0.75 age-1 3*0.5 = 1.5 age-2 3*0.25 = 0.75 age-3 What to do now? 7 Age Length Key
Age-Length Key Fractionation Fractionation When a fraction of a fish should be assigned a given age. Handling fractionation Round all values down to integers. For remaining number of fish, choose random ages in proportion to the proportion in each age. 8 Age Length Key
Age-Length Key Fractionation Handling fractionation Round all values down to integers. 30-cm 3*0.25 = 0.75 = 0 age-1 3*0.5 = 1.5 = 1 age-2 3*0.25 = 0.75 = 0 age-3 For remaining number of fish ... two ages must be chosen such that age-1 has 25% chance, age-2 has 50% chance, and age-3 has 25% chance of being selected. e.g., 2, 1 was chosen thus, randomly assign 1 age-1, 2 age-2, & 0 age-3 for fish in the 30-cm length interval 9 Age Length Key
Concept Age-Length Key Age-Length Key (as a reminder) LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50 Length Sample len age 23 25 26 28 32 33 36 40 43 44 48 49 51 54 LCat 20 20 20 20 30 30 30 40 40 40 40 40 50 50 1 2 2 1 2 Length distribution (as a reminder) LCat 20 30 40 50 Freq 4 3 5 2 Identify number in each length category to be assigned each age 1 2 1 2 0 30-cm 3*0.25 = 0.75 age-1 3*0.5 = 1.5 age-2 3*0.25 = 0.75 age-3 Randomly determine which fish are assigned these ages. 10 Age Length Key
Concept Age-Length Key Age-Length Key (as a reminder) LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50 Length Sample len age 23 25 26 28 32 33 36 40 43 44 48 49 51 54 LCat 20 20 20 20 30 30 30 40 40 40 40 40 50 50 1 2 2 1 2 Length distribution (as a reminder) LCat 20 30 40 50 Freq 4 3 5 2 Identify number in each length category to be assigned each age 1 2 3 1 2 3 3 1 1 3 40-cm 5*0.25 = 1.25 = 1 age-1 5*0.25 = 1.25 = 1 age-2 5*0.5 = 2.5 = 2 age-3 Extra fish was chosen to be age-3. Randomize age assignments. 11 Age Length Key
Concept Age-Length Key Age-Length Key (as a reminder) LCat 1 2 3 20 0.50 0.50 0.00 30 0.25 0.50 0.25 40 0.25 0.25 0.50 50 0.00 0.50 0.50 Length Sample len age 23 25 26 28 32 33 36 40 43 44 48 49 51 54 2 LCat 20 20 20 20 30 30 30 40 40 40 40 40 50 50 1 2 2 1 2 Length distribution (as a reminder) LCat 20 30 40 50 Freq 4 3 5 2 Identify number in each length category to be assigned each age 1 2 3 1 2 3 3 3 50-cm 2*0.5 = 1 age-2 2*0.5 = 1 age-3 Randomize age assignments. 12 Age Length Key
Utility Lengths in age sample should cover range of lengths in length sample. Age sample and length sample must be from the same population. typically age sample is a subsample Extra effort should be put in age, not length, sample. Combine age sample and age-assigned length sample for further analysis. 13 Age Length Key
