Discriminant Function Analysis

What is discriminat function analysis? That, I don't know. Here are some various explanations of a complex form of figuring out the differences between two like groups, based on the breakdown of their differences. Apparently you can predict where the group membership of two groups that are seemingly the same came from based on single or multiple variables. Or you can predict what characters are likely to differentiate those two like groups.

The main purpose of a discriminant function analysis is to predict group membership based on a linear combination of the interval variables. The procedure begins with a set of observations where both group membership and the values of the interval variables are known. The end result of the procedure is a model that allows prediction of group membership when only the interval variables are known. A second purpose of discriminant function analysis is an understanding of the data set, as a careful examination of the prediction model that results from the procedure can give insight into the relationship between group membership and the variables used to predict group membership.

If discriminant function analysis is effective for a set of data, the classification table of correct and incorrect estimates will yield a high percentage correct. Discriminant function analysis is found in SPSS under Analyze, Classify, Discriminant. One gets DA or MDA from this same menu selection, depending on whether the specified grouping variable has two or more categories.
Multiple discriminant analysis (MDA) is an extension of discriminant analysis and a cousin of multiple analysis of variance (MANOVA), sharing many of the same assumptions and tests. MDA is used to classify a categorical dependent which has more than two categories, using as predictors a number of interval or dummy independent variables. MDA is sometimes also called discriminant factor analysis or canonical discriminant analysis.

Stepwise Discriminant Analysis

Probably the most common application of discriminant function analysis is to include many measures in the study, in order to determine the ones that discriminate between groups. For example, an educational researcher interested in predicting high school graduates' choices for further education would probably include as many measures of personality, achievement motivation, academic performance, etc. as possible in order to learn which one(s) offer the best prediction.

Model. Put another way, we want to build a "model" of how we can best predict to which group a case belongs. In the following discussion we will use the term "in the model" in order to refer to variables that are included in the prediction of group membership, and we will refer to variables as being "not in the model" if they are not included.

Forward stepwise analysis. In stepwise discriminant function analysis, a model of discrimination is built step-by-step. Specifically, at each step all variables are reviewed and evaluated to determine which one will contribute most to the discrimination between groups. That variable will then be included in the model, and the process starts again.

Backward stepwise analysis. One can also step backwards; in that case all variables are included in the model and then, at each step, the variable that contributes least to the prediction of group membership is eliminated. Thus, as the result of a successful discriminant function analysis, one would only keep the "important" variables in the model, that is, those variables that contribute the most to the discrimination between groups.

F to enter, F to remove. The stepwise procedure is "guided" by the respective F to enter and F to remove values. The F value for a variable indicates its statistical significance in the discrimination between groups, that is, it is a measure of the extent to which a variable makes a unique contribution to the prediction of group membership. If you are familiar with stepwise multiple regression procedures, then you may interpret the F to enter/remove values in the same way as in stepwise regression.

Capitalizing on chance. A common misinterpretation of the results of stepwise discriminant analysis is to take statistical significance levels at face value. By nature, the stepwise procedures will capitalize on chance because they "pick and choose" the variables to be included in the model so as to yield maximum discrimination. Thus, when using the stepwise approach the researcher should be aware that the significance levels do not reflect the true alpha error rate, that is, the probability of erroneously rejecting H0 (the null hypothesis that there is no discrimination between groups).

Thats it, I'm out like a variable.

Greenland Musk Ox

The very qualities that made the musk ox survive for millions of years was the cause of their demise in Alaska. They tend to form a circle as a defense, where the young stay in the center. Awesome survival technique, but no match for market hunters in the 1800s.


The return of muskoxen to Alaska is an important success story in wildlife conservation. The original Alaska muskoxen disappeared in the mid- or late 1800s as they had much earlier in Europe and Asia. Overhunting likely contributed to their demise, at least in some areas. By the 1920s, muskox distribution was reduced to arctic Canada and East Greenland where a high take by whalers, hide hunters, and natives continued. Concern over the impending extinction of the species worldwide led to a move to restore a protected population to Alaska. In 1930, 34 muskoxen captured in East Greenland were brought to Fairbanks. In 1935 and 1936, all survivors and their calves were transported from Fairbanks to Nunivak Island and released. Muskoxen thrived on Nunivak Island and increased from 31 in 1936 to an estimated 750 by 1968.



Muskoxen from Nunivak Island were intended to provide stock for relocating animals to formerly occupied ranges. Nunivak Island muskoxen have been transplanted to the Arctic National Wildlife Refuge, Cape Thompson, the Seward Peninsula, Nelson Island, and to Wrangel Island and the Taimyr Peninsula in Russia. Additional animals have been donated to zoos and other institutions.





How else could the Musk ox have rebounded? With the help of these transplants and a hunting ban for decades and limited permited hunts they're doing good now. The market hunting during the Whaling period didn't help but to exterpate the species out of Alaska in the late 1800s. Whew, glad the European whalers are gone.





Maybe in some instances...the musk oxen of the Seward Peninsula in northwest Alaska love sex. How else to explain how one of the biggest success stories among large Alaska wildlife -- particularly a species that produces just one calf a year. In 1980, just 104 musk oxen roamed the peninsula, according to the Alaska Department of Fish and Game. Today, after 25 years of very restricted hunting, that number is nearly 3,000 animals.



"It's phenomenal," said wildlife biologist Brad Shults of the National Park Service, who is studying them as part of a project to compare the population and ecology of musk oxen on and adjacent to Bering Land Bridge National Preserve to those around Cape Krusenstern National Monument along the Chukchi Sea near Kotzebue. "It was averaging around 16 percent a year, although once we starting clipping the population with hunting, it leveled off."





Thats it, I'm out like the Whalers.

Karsting the First Stone

Thanks to those at Toolik Field Station, and its Environmental Data Center, I'm much more aware of studies going on in the Arctic.

About the Environmental Data Center
The TFS Environmental Data Center (EDC) offers support to the science community in three ways; 1) collection of long-term baseline environmental and biological data, 2) management of common-use laboratory and field equipment, and 3) limited assistance with field work. The EDC was developed to meet the needs of an expanding scientific community (Science Support - Direction for Next 10 Years ).

Karsting the first stone
The project, which is led by Breck Bowden of the University of Vermont in Burlington, involves 17 research groups from America and Canada. To start with, they will use a combination of aerial photography, field measurements, and ground- and satellite-based sensors to compile a map of all the thermokarstic areas of Alaska. This will provide a reference point from which changes can be measured.

The team will then try to work out how the development of features such as “retrogressive thaw slumps” and “active-layer detachments” (different ways in which thawing permafrost can cause a hillside to slip) are associated with the local climate, geology and vegetation. They will look, too, at the amount of ice in the ground, and the temperature and the moisture of the soil. All these data will be fed into computer models which, the researchers hope, will allow them to develop an automated way of predicting where and when new features will form, and to monitor them when they appear.

Dr Bowden and his colleagues also hope to understand the impact of thermokarst activity on the structure of the soil, and its nutrient content. They will concentrate on a few sites that can be studied intensively and which are affected by different types of activity. They will measure the amount of carbon, phosphate and nitrate in the soil, together with the rate of plant growth and microbial decomposition. That will let them work out just how “leaky” thawing permafrost is and thus how big its contribution of greenhouse gases to the atmosphere might be, should the worst come to the worst.

It will also help them forecast changes in the tundra’s vegetation. The softening of the soil and the consequent release of nutrients is likely to encourage the growth of shrubs on land that is now dominated by grass, moss and lichens. The researchers will monitor the growth of this vegetation around newly formed thermokarst features and use experimental field plots to test how conditions mimicking such features affect which species will thrive.

Last, the project will try to work out how thawing permafrost will affect the numerous streams, rivers and lakes of the Arctic. Together, these amount to the biggest acreage of water on “dry” land. As water moves through affected areas, it picks up both nutrients and sediment that would otherwise be held in the permafrost’s icy grasp. These, paradoxically, have opposite effects on the growth of algae. The phosphates and nitrates stimulate it whereas the extra sediment suppresses it by trapping nutrients in the beds of such bodies of water.

Rest of the story @ The Economist.

Thats it, I'm out like Permafrost in the Arctic.

Louis Kissel

On June 5th, 1906, Louis Kissel and his sons decided to get into the automobile business and formed the Kissel Motor Car Company, based in Hartford Wisconsin. Their first car, The Kissel Kar, was offered in 1907. The Kissel Kar had a conventional four-cylinder, 35-horsepower water cooled engine. They were a bit unusual in that they began making almost all of the components for its cars themselves, including the engines. In 1909, a six-cylinder model was introduced, electric starters were added in 1913, and a short-lived Double Six V-12 was introduced in 1917.
.1921 Kissel Tourster



The company's reputation was based on quality, durability, advanced design, outstanding performance, and dependability, which they were able to provide because they were a low production company. The name Kar was dropped during WWI, as anything that sounded German was unpopular at that time.



Kissel also produced a model called the All-Year. It had a removable hardtop with glass windows and curtains. It made the Kissel into a closed car, and passengers enjoyed the protection from the elements.Kissel's look began to change in 1917, under the guidance of Conover T. Silver, the New York Kissel distributor and part-time designer. With his encouragement, Kissel developed the Kissel Kar Silver Special Speedster in 1918, named after Mr. Silver himself.





Amelia Earhart happened to own a 1923 Kissel Speedster(Gold Bug). Amelia and her mother left Los Angeles for Boston in May 1924, traveling through Sequoia, Yosemite, Lake Louise and Banff. They drove across Canada and arrived in Boston 6 weeks later.



Considering the condition of roads at that time and the rarity of mechanical help, especially in the more remote areas, this was a daring adventure covering 7,000 miles and covering the car with tourist stickers. Cross-continental travel by automobile was still a novelty, so Amelia and her mother were continually stopped by people and asked many questions.



She found the bright yellow car, unremarkable in Los Angeles, to draw attention across the country. "The fact that my roadster was a cheerful canary color may have caused some of the excitement. It had been modest enough in California, but was a little outspoken for Boston, I found."





This yellow bug happens to be at the Korney Museum of Transportation East of Denver, at East Colfax.

Thats it, I'm out like the Double 6 V-12.

Can't you See??

Can't you See??

Love Kid Rock's Version.