1 / 53

Analysis of Alpaca Fiber Data

Analysis of Alpaca Fiber Data. By Ying Luo and Kristen Swinton. Background. Alpacas are Llama-like animals bred in South America from which fibers are collected to make wool. Different properties of the fibers affect the quality of the wool. Response Variables.

tayte
Download Presentation

Analysis of Alpaca Fiber Data

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Analysis of Alpaca Fiber Data By Ying Luo and Kristen Swinton

  2. Background • Alpacas are Llama-like animals bred in South America from which fibers are collected to make wool. • Different properties of the fibers affect the quality of the wool.

  3. Response Variables • Our client was interested in both the tensile strength and the scale of the fibers. • Tensile strength is a measure of the breaking strength of the fiber. • Scale is a measure of the distance between the “scales,” or cells on the surface of the fiber.

  4. More About Scales • The scales are important as they help the fibers interlock to form felt. • Fibers with more scales—and consequently a shorter distance between them—are more likely to have been damaged. • Hence, a higher scale measure indicates healthier fibers.

  5. Explanatory Variables • The client suspected that the breed of Alpaca used and the diet it is fed might affect the tensile strength and scale of the fibers. • Data was collected for 22 Alpacas of two breeds—Suri and Huacaya.

  6. Explanatory Variables • One of the diets of interest is a diet meant to simulate the diet of an animal in the wild. This diet is referred to as the “low nutrition diet.” • The other diet is a more typical diet of animals raised in captivity. This is the “high nutrition diet.”

  7. Covariates • Data was also collected on the animals’ gender, age at the beginning of the study, and color. • These factors were included in the analysis along with the original explanatory variables.

  8. Complications • Many observations were taken on each animal. To simplify the analysis, we took the mean tensile strength and mean scale for each animal. • Breed and gender were confounded—there were no female Suris in the sample. • Unbalanced data further complicated the analysis.

  9. Time Periods • Data was collected one year after the study began. This is called period four. • More data was collected two years into the study. This is period eight. • We analyzed each set of data separately and compared the results.

  10. Strategy of Analysis • We started with the tensile strength data. • After analyzing the complete set of data, we analyzed two subsets—males only and whites only. • The males only analysis was done to eliminate the breed and gender confounding. • The whites only analysis was suggested by the client in an attempt to balance the data.

  11. Tensile Strength AnalysisComplete Data • We started with the data from period four. • We first tried to fit models with only one factor and assess their significance. • Two factors had significant F-tests: breed and gender. • A gender only model does not give any information about the factors of primary interest.

  12. Complete Data • Diet was not significant alone, but did have a significant interaction with gender. • It appears that the low nutrition diet produced higher tensile strengths for both genders.

  13. Complete Data • As with diet, color did not have a significant effect on tensile strength by itself. • It did, however, interact with breed.

  14. = m + + e Y B ij i ij Possible Models Model 1 F = 21.59 p-value = 0.0002 Model 2 F = 6.42 p-value = 0.0024 Model 3 F = 8.02 p-value = 0.0006

  15. Period Eight • The period eight data produced the same three models. • The p-values were a bit larger, but still significant at the 0.05 level. • This suggests no significant effect of the passage of one year.

  16. Males Only—Period Four • Model 1 (breed only) had a p-value of 0.0036. • Because this data only has one gender, there is no longer any confounding of breed and gender. • Since this model is significant, there may be a true breed effect.

  17. Other Males Only Models • Model 2 is no longer appropriate since it includes the gender effect. • In examining Model 3, we noticed that the breed by color interaction was no longer significant. • This is possibly because nearly all the Huacaya males were white, while there was only one white Suri male.

  18. Period Eight • Similarly to period four, only Model 1 fit the data reasonably well. • Its p-value was 0.0755, which is greater than 0.05, but the sample size was rather small (14).

  19. Whites Only—Period Four • Model 1 was again highly significant with a p-value of 0.0009. • In fitting Model 2, we discovered that the diet by gender interaction was no longer significant. • The reason for this is unclear, but could be due to confounding of color with either diet or gender. • Model 3 is clearly not applicable here as it contains a color main effect.

  20. Whites Only—Period Eight • Results were similar to those of period four. • The p-value for Model 1 was 0.0085.

  21. Tensile Strength Conclusions • Breed appeared to be an important factor in all the models. • A boxplot of the distribution of tensile strength for each breed illustrates this apparent effect.

  22. Breed or Gender? • Because of the confounding, we cannot be sure that the apparent effect is truly due to breed. • A plot of the tensile strength for each breed of the males only data can clarify this issue.

  23. Summary of Tensile Strength Conclusions • Breed seems to have a significant effect on tensile strength, but it is confounded with gender. • In looking at the males only, this effect is still present. • This effect is the same when white animals are examined alone. • Huacayas produce fibers with higher tensile strength on average than do Suris.

  24. Analysis of Scale Data • Analysis was more difficult for the scale data, with different subsets producing different models. • We began our analysis as before by looking for single factor models for the period four data first. • The only single factor with a significant F-test was age.

  25. Scale Data—Complete • As with the tensile strength data, there was a significant interaction between diet and gender. • The low nutrition diet produces higher scale for males, but lower scale for females.

  26. Scale Data—Complete • Color was not significant by itself, but it was significant when added to the age only model. • There was no significant interaction between color and age.

  27. Possible Models Model 4 F = 5.35 p-value = 0.0315 Model 5 F = 3.48 p-value = 0.0300 Model 6 F = 4.44 p-value = 0.0085

  28. Period Eight • Model 4 (age only) fit well with a p-value of 0.0018 • Model 5 no longer fit because there was no longer a significant diet by gender interaction. • Gender, however, still had a significant effect when added to the age only model, but there was no age by gender interaction. • This may be another side effect of the unbalanced data.

  29. Period Eight • Although it did not fit well for period four, the breed only model (Model 1) fit the period eight data quite well. • Another significant model contained the main effects for age and breed, but not their interaction.

  30. Period Eight Models Model 4 F = 12.99 p-value = 0.0018 Model 7 F = 9.39 p-value = 0.0015

  31. Period Eight Models Model 1 F = 6.67 p-value = 0.0163 Model 8 F = 11.19 p-value = 0.0006

  32. Data Problems • There were a couple of rather large observations, which upon investigation appeared to be mistakes. • The client agreed that they were probably recording mistakes, so we threw them out.

  33. Other Problems • The standard deviation of the measurements in period eight was half that of period four (after outliers were discarded). • This could be due to the data collector becoming more skilled in operating the machinery.

  34. Males Only—Period Four • Neither Model 4 nor 6 fit the data well. • A diet only model became significant for the males only. • A diet by breed interaction was also significant for the males only.

  35. Males Only Models—Period Four Model 9 F = 8.05 p-value = 0.0150 Model 10 F = 8.06 p-value = 0.0048

  36. Males Only—Period Eight • In period eight, the diet only model (Model 9) was no longer significant. Model 10 was not significant either. • The age only model (Model 4) had a p-value of 0.0276. • Model 1 (breed only) had a p-value of 0.0954 which is not strictly significant, but is worth noting.

  37. Whites Only—Period Four • The only model that had a significant F -test for the white animals only was a model containing the main effects of age and diet along with their interaction.

  38. Whites Only—Period Eight • Curiously, the model that fit the period four data did not fit the period eight data very well. • The only model that had a reasonable fit was the breed only model (Model 1) with a p-value of 0.0513.

  39. Whites Only Models Model 11 (Period 4) F = 6.88 p-value = 0.0132 Model 1 (Period 8) F = 4.9 p-value = 0.0513

  40. Scale Conclusions • It is difficult to make overall conclusions about the factors affecting scale. • One factor that appeared in most models was age. • This suggests that age does have some effect on scale. • How age interacts with the other factors is not clear.

  41. Effect of Age • It appears that older animals have lower scale measurements than younger animals. • This suggests that older animals have more damaged fibers.

  42. Scale Conclusions • The other effect worth mentioning is the breed effect. • It was not significant in period four, but had moderate significance in period eight. • Suris seem to have higher scale measurements than Huacayas, on average.

  43. Diagnostics • It would be impractical to do residual analyses for all eleven models fit to all six subsets of data. • Since the client was primarily interested in the white animals, we only checked the residuals for the four models fit to the whites only data.

  44. Model 1—Tensile StrengthPeriod Four • A normal probability plot of the data had one unusual observation with a residual of –3.59. • The animal (W-35) that generated this observation had an unusually small tensile strength. • There was no reason to eliminate the point. • Our assumption of normally distributed errors, therefore, may not be valid. Conclusions should be accepted with caution.

  45. Model 1—Tensile StrengthPeriod Four • A plot of residuals vs. fits also indicated this unusual observation. • If that point is ignored, the variance appears constant.

  46. Model 1—Tensile StrengthPeriod Eight • The normal probability plot for period eight looked much better than the one for period four. • The residual for W-35 was –2.98. • The scale measurement for this observation was similar for both time periods. • The residuals vs. fits plot also looked better.

  47. Model 11—ScalePeriod Four • The normal probability plot had a possible outlier. • The residual for this outlier was only –1.67 —not too worrisome. • The residual vs. fits plot looked okay.

  48. Model 1—ScalePeriod Eight • The normal probability plot was not quite linear, but had no obvious outliers. • Since the F-test is robust for violations of the normality assumption, we feel that this is not a problem. • The residual vs. fits plot showed no evidence of non-constant variance.

  49. Final Conclusions • It appears that breed is a significant predictor of tensile strength, despite its confounding with gender. • Huacayas generally produce fibers of higher tensile strength than Suris.

  50. Final Conclusions • Conclusions for the scale data are not definite. • Age seemed to be a significant predictor, with older animals producing fibers with lower scale. • Breed was somewhat significant for period eight, but not for period four. • For period eight, Suris have higher scale measurements than Huacayas.

More Related